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189 Cards in this Set

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The separation between atoms at which the attraction ends and the repulsion begins is their
equilibrium separation, that is, the separation at which the atoms exert no forces on one another
energy stored in the chemical forces between atoms:
The bound atoms have become:
chemical potential energy;a molecule. The strength of their bond is equal to the amount of work the atoms did when they drew together or, equivalently, the work required to separate them.
Like all liquids and solids, our burning log is just a huge assembly of atoms and molecules, held together by chemical bonds of various strengths. These particles push and pull on one another as they vibrate about their equilibrium separations. Their motion is:
If no thermal energy flows when two objects touch, then those objects are in:
thermal motion, and the energy involved in this disorderly jiggling is thermal energy. Because thermal energy is fragmented among the atoms and exchanged between them unpredictably, it can't be used directly to do work. 2.thermal equilibrium and their temperatures are equal.
But how does burning wood produce thermal energy? A woodstove is an example of a:
This thermal energy is released by a chemical reaction between molecules in the wood and oxygen in the air. 2. heat exchanger—a device that transfers heat without transferring the hot molecules themselves.
Conduction occurs when
heat flows through a stationary material. The heat moves from a hot region to a cold region but the atoms and molecules don't.
Heat is thermal energy on the move. Strictly speaking, the burning log doesn't contain heat:
2. woodstove is an example of a heat exchanger:
it contains thermal energy. 2. device that transfers heat without transferring the hot molecules themselves.
Thermal conductivity is: _____ 2.Conduction is what moves thermal energy from the woodstove's inside to its outside...
the measure of how rapidly heat flows through a material when it's exposed to a difference in temperatures. 2. No atoms move through the metal walls of the stove, just heat.
Convection occurs when a moving fluid transports heat from a: ____. 2. This moving air is a convection current:
hotter object to a colder object. The heat moves as thermal energy in the fluid so that the two travel together. The fluid usually follows a circular path. 2. the looping path that it follows is a convection cell.
The types of electromagnetic waves in an object's thermal radiation depend on its temperature...
While a colder object emits only radio waves, microwaves, and infrared light, a hotter object can also emit visible or even ultraviolet light.
When two objects face one another, thermal radiation will travel in both directions between them. However, the hotter object will dominate this radiant exchange of thermal energy, resulting in...
in a net transfer of thermal energy to the colder object. Exchanges of thermal energy via radiation always transfers heat from a hotter object to a colder one.
The constant of proportionality is called:
heat capacity and is the amount of heat that must be added to the bowl to cause its temperature to rise by 1 unit. In effect, the bowl's heat capacity is the measure of its thermal sluggishness, its resistance to temperature changes.
It makes sense to characterize each material by its heat capacity per unit mass, a quantity known as: ______. 2. Each material's specific heat depends principally on the number of microscopic ways it can store thermal energy per kilogram. Known as a:
specific heat. The SI unit of specific heat is the joule-per-kilogram-kelvin (abbreviated J/kg · K). Each bowl's heat capacity is the product of its mass times the specific heat of the material from which it's made. 2. degree of freedom, each independent way of handling thermal energy stores an average thermal energy equal to half the Boltzmann constant times the absolute temperature (½kT).
Like most solids, ice is crystalline:
its water molecules are arranged in an orderly latticework that extends over long distances and gives rise to the beautiful crystal facets seen on snowflakes and frost. Ice's crystalline structure is so constraining that its water molecules can't use thermal energy to change bonding partners and consequently ice can't change shape.
The solid phase of a typical substance is thus denser than the liquid phase of that same substance, so the solid phase sinks in the liquid phase.
The heat used to transform a certain mass of solid into liquid, without changing its temperature, is called the:
latent heat of melting or, more formally, latent heat of fusion. The bonds between the water molecules in ice are strong enough to give ice an enormous latent heat of melting.
Ice's huge latent heat of melting has a stabilizing effect on:
the phase equilibrium between ice and water. Whenever ice and water are mixed together, the mixture's temperature will shift rapidly toward 0 °C.
Since the molecules in water cling to one another with chemical bonds, it takes energy to separate them. Although the bonds between water molecules...
are weaker than the bonds within water molecules, it still takes a great deal of energy to transform water into steam.
The heat needed to transform a certain mass of liquid into gas, without changing its temperature, is called the:
latent heat of evaporation or, more formally, latent heat of vaporization. Water's latent heat of evaporation is truly enormous because water molecules are surprisingly hard to separate. About 2,300,000 J of heat is needed to convert 1 kg of water at 100 °C into 1 kg of steam at 100 °C.
The latent heat of evaporation reappears when steam condenses and the gathering...
water molecules release their chemical potential energy as heat. The heat released when transforming a certain mass of gas into liquid, without changing its temperature, is again the latent heat of evaporation. You must add a certain amount of heat to water to evaporate it and you must remove that same amount of heat from steam to condense it.
The basic indicator of whether water will evaporate or steam will condense is relative humidity...
Relative humidity measures the water molecule landing rate as a percentage of the leaving rate. When the relative humidity is 100%, the two rates are equal and water and steam are in phase equilibrium. Relative humidity depends on the temperature and on the density of the steam.
Steam at its equilibrium density is said to be: 2. The saturated steam's density, together with its temperature, determine its:
saturated. 2. pressure—the pressure inside our container. If we warm the container, the density of the saturated steam will increase and so will its pressure.
But when the water temperature is near 100 °C, something remarkable happens: saturated steam bubbles suddenly become stable and the water can begin to:
boil. At that temperature, water's boiling temperature, the pressure of saturated steam reaches atmospheric pressure and bubbles of saturated steam can survive indefinitely within the water. Even more remarkably, these bubbles can grow by evaporation; each bubble's surface is an interface between water and steam, so when heat is added to the water, water can transform into steam and enlarge the bubble. Although the bubbles quickly float to the water's surface and pop, new bubbles can promptly take their place.
Because nucleation: ___. 2. Once boiling stops, the water's temperature can rise above the boiling temperature so that it becomes:
seed-bubble formation almost never occurs spontaneously in water below 300 °C, something else must create those seeds. Most nucleation occurs at defects or hotspots on the container or at contaminants in the liquid. 2. superheated.
There is one other interesting way to change water's boiling temperature:
A dissolved chemical keeps the water molecules busy so that they are less likely to leave the water to become steam, or ice for that matter. Since dissolved chemicals discourage water molecules from leaving water's liquid phase, they suppress any phase transitions that reduce the amount of liquid phase water.
Light from an incandescent lightbulb is part of the:
thermal radiation emitted by its hot wire filament. While most types of electromagnetic waves are invisible, our eyes are sensitive to a narrow range of waves that we call visible light.
To reproduce pure white sunlight, the bulb's filament should be heated to 5800 °C. Unfortunately, nothing is solid at that high temperature. Even tungsten metal, the best filament material known, readily sublimes at temperatures:
2500 °C(4500 °F). Since incandescent lightbulbs must operate at lower temperatures, they can't really reproduce sunlight. Most give off the warm, yellow-white light that's characteristic of tungsten metal at about 2500 °C.
The distribution of wavelengths emitted by the filament depends on its temperature and surface properties, particularly its:
emissivity—the efficiency with which it emits and absorbs light. Emissivity is measured on a scale from 0 to 1, with 1 being ideal efficiency.
The distribution of wavelengths emitted by a black object is determined by its temperature alone and is called a:
blackbody spectrum. An object that isn't black emits somewhat less thermal radiation, but that radiation still brightens and shifts toward shorter wavelengths as the object becomes hotter.
The temperature associated with a particular distribution of wavelengths is the:
color temperature of that light. We can already see two of the principal shortcomings of an incandescent lightbulb: its poor efficiency at converting electric energy into visible light and its low color temperature. At 2500 °C, only about 12% of its thermal radiation is visible light; the rest is invisible infrared light.
The temperature at which this heat balance occurs is surprisingly specific. That's because the filament's thermal radiation...
so rapidly with temperature that even a small excursion above its normal operating temperature will cause the filament to radiate away more thermal energy than it produces from electricity and it will quickly cool back down to normal.
warmer the ice, the more often water molecules at its surface can...
gather enough thermal energy to break free and leave. Below ice's melting temperature, water molecules leave the ice too infrequently to balance the landing process and the water transforms completely into ice.
Ice's huge latent heat of melting has a stabilizing effect on the phase equilibrium between ice and water...
Whenever ice and water are mixed together, the mixture's temperature will shift rapidly toward 0 °C.
Although the bonds between water molecules are weaker than the bonds...
within water molecules, it still takes a great deal of energy to transform water into steam.
The heat needed to transform a certain mass of liquid into gas, without changing its temperature, is called the: ________. 2. The latent heat of evaporation reappears when steam condenses and the gathering water molecules.
latent heat of evaporation or, more formally, latent heat of vaporization. Water's latent heat of evaporation is truly enormous because water molecules are surprisingly hard to separate. 2. release their chemical potential energy as heat.
When the relative humidity is below 100%, ice sublimes. When the weather is cold and dry, snow gradually disappears from the ground without ever melting...
And when you leave food unprotected in that same frostless freezer, it eventually dries out. vs. And when the relative humidity exceeds 100%, steam deposits. And snowflakes grow in clouds and then descend gracefully to the ground.
Steam at its equilibrium density is said to be: ____. 2. Light from an incandescent lightbulb is part of the:
2. thermal radiation emitted by its hot wire filament. object that's hotter than about 400 °C(750 °F) emits enough visible light for us to see it in a dark room.
To reproduce pure white sunlight, the bulb's filament should be heated to 5800 °C. Unfortunately:
othing is solid at that high temperature. Even tungsten metal, the best filament material known, readily sublimes at temperatures above 2500 °C(4500 °F).
To keep the white-hot filament from burning, it's surrounded by a glass bulb that usually contains:
oxygen-free inert gas. This gas, typically nitrogen and argon, slows sublimation by bouncing some of the escaping tungsten atoms back onto the filament. Although the gas extends the filament's life, it has at least two drawbacks. First, it allows conduction and convection to carry some heat away from the filament. Second, tiny tungsten particles that form in this gas rise with convection currents to produce a dark spot on the top of the bulb.
material's thermal expansion is caused by atomic vibrations. Because of thermal energy, adjacent atoms vibrate back and forth about their equilibrium separations (Fig. 7.3.6). This vibrational motion isn't symmetric:
the repulsive force the atoms experience when they're too close together is stiffer than the attractive force they experience when they're too far apart. As a result of this asymmetry, they push apart more quickly than they draw together and thus spend most of their time at more than their equilibrium separation. On average, their actual separation is larger than their equilibrium separation, and the material containing them is bigger than it would be without thermal energy.
As an object's temperature rises, its atoms move farther apart on average and the object grows larger in all directions. The extent to which an object expands with increasing temperature is normally described by its:
coefficient of volume expansion: the fractional change in the object's volume per unit of temperature increase. Fractional change in volume is the net change in volume divided by the total volume.
One way to prolong the life of the filament is to increase its surface area while providing it with the...
same electric power. With more surface area to radiate away thermal power, the filament doesn't get quite as hot and doesn't sublime as quickly. The result is an extended life bulb. Unfortunately, extended life bulbs are redder than conventional bulbs and also less energy efficient. Because an extended life bulb emits a smaller fraction of its input power as visible light, it must have a higher wattage to give equivalent lighting. As a result, extended life bulbs aren't always a bargain; the money you save on replacement bulbs may well be spent on increased energy costs.
When you're choosing bulbs, it's worth looking at how many:
lumens—the measure of useful illumination—they produce per watt of electric power consumed.
You're much better off buying a halogen bulb, which is both longer-lived and more energy efficient than a conventional bulb. A halogen bulb uses a:
chemical trick to rebuild its filament continuously during operation. This filament is enclosed in a small tube of quartz or aluminosilicate glass, which can tolerate high temperatures and reactive chemicals. The tube contains molecules of the halogen elements bromine and/or iodine. During operation, the tube becomes extremely hot and the halogen reacts with any tungsten atoms on its inside surface. They form a gas of tungsten–halogen molecules that drift about the tube until they encounter the white-hot filament. The molecules then break apart and the tungsten atoms stick to the filament.
The halogens act as recycling agents, seeking out tungsten atoms that have sublimed from the filament and returning them to it. Unfortunately, this recycling process slowly changes the structure of the filament...
The returning tungsten atoms deposit unevenly, so that the filament gradually develops thin spots and eventually burns out. Nonetheless, the filament lives more than 2000 hours, even when it runs several hundred degrees hotter than in a conventional bulb. Its higher filament temperature allows a halogen bulb to produce whiter light than a conventional bulb and increases its energy efficiency.
1. Bulbs with different power ratings have filaments with different amounts of surface area. The filament in a 100-W bulb has four times the surface area of the: ____. 2. One way to make an incandescent bulb with a variable light output is to put several independent filaments in it.
1. filament in a 25-W bulb and thus emits four times as much light. 2. A “three-way bulb” has two filaments (Figs. 7.3.9 and 7.3.10) that can be turned on and off separately. In a 50-100-150 W bulb, one filament uses 50W of electric power and the other uses 100 W.
Observations about Lightbulbs
Thermal Radiation
Filament Temperature and Color
Power and Light
Three-Way Bulbs
Filament Requirements
Tungsten’s Shortcomings
Sealing Issues
Halogen Bulbs
Halogen bulbs recycle tungsten...
Specialized Bulbs
Energy-saver bulbs – underwattage gimmicks
Water and Steam
destabilize water relative to
adding heat
or reducing steam density. 2. destabilize steam relative to water
Boiling (Part 1)
Ice and Steam
Ice and Steam (con’t)
Effects of Impurities
Burning Wood
Chemical Reactions
the average
thermal kinetic energy per particle 2. mobile electrons carry heat long distances
heat flows quickly from hot to cold spots
Conduction moves heat through stove’s walls
Convection and Woodstoves
Radiation and Woodstoves
The Zeroth Law of Thermodynamics 2. The First Law of Thermodynamics
Two objects that are each in thermal equilibrium with a third object are also in thermal equilibrium with one another. 2. The change in a stationary object's internal energy is equal to the heat transferred into that object minus the work that object does on its surroundings.
The Second Law of Thermodynamics
The entropy of a thermally isolated system of objects never decreases. Because of the second law, the only way to cool your home is to export its thermal energy and entropy elsewhere. Such a transfer would be easy if you had a cold object nearby to receive the heat.
The Third Law of Thermodynamics
As an object's temperature approaches absolute zero, its entropy approaches zero.
In most cases, the air conditioner uses a fluid to transfer heat from the colder indoor air to the hotter outdoor air. Known as the working fluid...
this substance absorbs heat from the indoor air and releases that heat to the outdoor air.

The working fluid flows in a looping path through the air conditioner's three main components: an evaporator, a condenser, and a compressor.
The evaporator is a heat exchanger that allows...
heat to flow from the warm air around it to the cool working fluid inside it. Its fins provide additional surface area to facilitate that heat flow and a fan blows the indoor air rapidly past the fins so that heat moves quickly into the working fluid.working fluid obtains that latent heat of evaporation from its own thermal energy, so its temperature drops and heat then flows into it through the walls of the evaporator. By the time the gaseous working fluid leaves the evaporator, it has absorbed a great deal of the indoor air's thermal energy and carries that energy with it as chemical potential energy.
As it flows through a pipe toward the evaporator, the working fluid's pressure is high and it's stable as a liquid. At this high pressure, any gaseous working fluid would be so dense that landing would dominate leaving and the gas would condense. Thus the pipe carries only high-pressure liquid working fluid to the evaporator...
But just before reaching the evaporator, the liquid working fluid passes through a narrow constriction in the pipe and its pressure drops dramatically. The low-pressure working fluid that results isn't stable as a liquid. At low pressure, any gaseous working fluid is so dilute that leaving dominates landing and the liquid evaporates. Thus as the low-pressure liquid working fluid emerges from the constriction and pours into the evaporator, it's evaporating rapidly. It continues to evaporate even though its temperature decreases as it absorbs its latent heat of evaporation.
Half the air conditioner's job is done: it has removed heat from the indoor air.
Satisfying the second law is the task of the compressor. The compressor receives low-pressure gaseous working fluid from the evaporator, compresses it to much higher density, and delivers it as a high-pressure gas to the condenser. The compressor may use a piston and one-way valves, like the water pump in Fig. 5.2.3, or it may use a rotary pumping mechanism. But regardless of how it functions, the result is the same: the gaseous working fluid undergoes a dramatic increase in density and pressure as it passes through the compressor...
Compressing a gas requires work because the compressor must push the gas inward while moving it inward—force times distance. Since work transfers energy, the compressor increases the energy of the gas. The air conditioner usually obtains this energy from the electric company and converts it into mechanical work with an electric motor.

In accordance with the first law of thermodynamics, this work increases the internal energy of the working fluid. The only way that the gaseous working fluid can store this additional energy is as thermal energy in its individual particles. These particles begin to move about more and more rapidly, so that the gaseous working fluid leaves the compressor much hotter than when it arrived. There is no getting around that temperature rise; compressing the working fluid unavoidably raises its temperature.
This hot, high-pressure working fluid then flows into the condenser. Like the evaporator, the condenser is a long metal pipe with fins attached to it. It acts as a heat exchanger and its metal fins provide extra surface area to speed the flow of heat from the hotter working fluid inside it to the less hot outdoor air. There may also be a fan to move outdoor air quickly past the condenser and speed up the heat transfer. As its name suggests, the condenser allows the gaseous working fluid inside it to condense into a liquid. Compression prompts that condensation. While it flows through a pipe toward the compressor, the low-pressure working fluid is stable as a gas. But in the high-pressure, high-density working fluid that emerges from the compressor, the landing rate far outpaces the leaving rate and the gas condenses.
Like any condensing substance, the gaseous working fluid releases its latent heat of evaporation as its molecules bind together and it transforms into a liquid. This latent heat of evaporation becomes thermal energy in the working fluid, so its temperature rises still further and heat flows out of it through the walls of the condenser.

By the time the liquid working fluid leaves the condenser, it has transformed a great deal of chemical potential energy into thermal energy and released that energy into the outdoor air. The outdoor air receives as heat not only the thermal energy extracted from the indoor air, but also the electric energy consumed by the compressor. The working fluid leaves the condenser as a warm, high-pressure liquid and travels through a pipe toward the evaporator.
The second half of the air conditioner's job is now complete: it has released heat into the outdoor air and, in the process, converted ordered energy into thermal energy. From here, the working fluid returns to the evaporator to begin the cycle all over again. Before leaving air conditioners, we should take a moment to look at the working fluid itself.
fluid must become a gas at low pressure and a liquid at high pressure, over most of the temperature range encountered by the air conditioner.
The car engine avoids conflict with the second law by being a heat engine:
a device that converts thermal energy into ordered energy as heat flows from a hot object to a cold object. While thermal energy in a single object can't be converted into work, that restriction doesn't apply to a system of two objects at different temperatures. Because heat flowing from the hot object to the cold object increases the overall entropy of the system, a small amount of thermal energy can be converted into work without decreasing the system's overall entropy and without violating the second law of thermodynamics.
As long as the engine delivers enough heat to the outdoor air to keep the total entropy from decreasing, there's nothing to prevent it from converting the remaining heat into ordered energy!
This conversion starts as soon as you remove your foot from the brake and begin to accelerate forward. Instead of transferring all of the thermal energy in the burning fuel to the outdoor air, your car then extracts some of it as ordered energy and uses it to power the wheels. The car engine can convert thermal energy into ordered energy, as long as it passes along enough heat from the hot object to the cold object to satisfy the second law of thermodynamics.

Obeying the second law becomes easier as the temperature difference between the two objects increases. When the temperature difference is extremely large, as it is in an automobile engine, a large fraction of the thermal energy leaving the hot object can be converted into ordered energy—at least in theory.
To extract work from the fuel, the internal combustion engine must perform four tasks in sequence:
It must introduce a fuel–air mixture into an enclosed volume.
It must ignite that mixture.
It must allow the hot burned gas to do work on the car.
It must get rid of the exhaust gas.
Automobile engines usually have four or more of these cylinders. Each cylinder is a separate energy source, closed at one end and equipped with a movable piston, several valves, a fuel injector, and a spark plug. The piston slides up and down in the cylinder, shrinking or enlarging the cavity inside. The valves, located at the closed end of the cylinder, open to introduce fuel and air into the cavity or to permit burned exhaust gas to escape from the cavity. The fuel injector adds...
fuel to the air as it enters the cylinder. And the spark plug, also located at the closed end of the cylinder, ignites the fuel–air mixture to release its chemical potential energy as thermal energy.
The fuel–air mixture is introduced into each cylinder during its induction stroke. In this stroke, the engine pulls the piston away from the cylinder's closed end so that its cavity expands to create a partial vacuum. At the same time, the cylinder's inlet valves open so that atmospheric pressure can push fresh air into the cylinder. The cylinder's fuel injector adds a mist of fuel droplets to this air so that the cylinder fills with a flammable fuel–air mixture. Because it takes work to move air out of the way and create a partial vacuum...
the engine does work on the cylinder during the induction stroke. At the end of the induction stroke, the inlet valves close to prevent the fuel–air mixture from flowing back out of the cylinder. Now the compression stroke begins. The engine pushes the piston toward the cylinder's closed end so that its cavity shrinks and the fuel–air mixture becomes denser.
In accordance with the first law of thermodynamics, this work increases the internal energy of the fuel–air mixture. That gaseous mixture can't store the added energy in potential form, so its thermal energy rises and it becomes hotter...
Since increases in a gas's density and temperature both increase its pressure, the pressure in the cylinder rises rapidly as the piston approaches the spark plug.
At the end of the compression stroke, the engine applies a high-voltage pulse to the spark plug and ignites the fuel–air mixture. The mixture burns quickly to produce hot, high-pressure burned gas, which then does work on the car during the cylinder's power stroke. In that stroke, the gas pushes the piston away from the cylinder's closed end so that its cavity expands and the burned gas becomes less dense. Since the hot gas exerts a huge pressure force on the piston as it moves outward, it does work on the piston and ultimately propels the car...
As it does work, the burned gas gives up thermal energy and cools in accordance with the first law of thermodynamics. Its density and pressure also decrease. At the end of the power stroke, the exhaust gas has cooled significantly and its pressure is only a few times atmospheric pressure. The cylinder has extracted much of the fuel's chemical energy as work.
The cylinder gets rid of the exhaust gas during its exhaust stroke. In this stroke, the engine pushes the piston toward the closed end of the cylinder while the cylinder's outlet valves are open. Because the burned gas trapped inside the cylinder at the end of the power stroke is well above atmospheric pressure, it accelerates out of the cylinder the moment the outlet valves open.
Just opening the outlet valves releases most of the exhaust gas, but the rest is squeezed out as the piston moves toward the cylinder's closed end. The engine again does work on the cylinder as it squeezes out the exhaust gas. At the end of the exhaust stroke, the cylinder is empty and the outlet valves close. The cylinder is ready to begin a new induction stroke.
The goal of an internal combustion engine is to extract as much work as possible from a given amount of fuel. In principle, all of the fuel's chemical potential energy can be converted into work because both are ordered energies.
Since the burned fuel is extremely hot, a good fraction of its thermal energy can be converted into ordered energy by diverting some of the heat that flows from the burned fuel to the outdoor air.
But a real internal combustion engine wastes energy and extracts less work than the second law allows. For example:
some heat leaks from the burned gas to the cylinder walls and is removed by the car's cooling system. This wasted heat isn't available to produce work. Similarly, sliding friction in the engine wastes mechanical energy and necessitates an oil-filled lubricating system. Overall, a real internal combustion engine converts only about 20% to 30% of the fuel's chemical potential energy into work.
To obtain the hottest possible burned gas, the compression stroke should squeeze the fuel–air mixture into as small a volume as possible. The more tightly the piston compresses the mixture, the higher its density, pressure, and temperature will be before ignition and the hotter the burned gases will be after ignition.
Since the efficiency of any heat engine increases as the temperature of its hot object increases and since the hot burned gas is the automobile engine's “hot object,” its high temperature after ignition is good, the hotter the better.
The extent to which the cylinder's volume decreases during the compression stroke is measured by its compression ratio—its volume at the start of the compression stroke divided by its volume at the end of the compression stroke.
Unfortunately, the compression ratio can't be made arbitrarily large. If the engine compresses the fuel–air mixture too much, the flammable mixture will become so hot that it will ignite all by itself. This spontaneous ignition due to overcompression is called preignition or knocking. When an automobile knocks, the gasoline burns before the engine is ready to extract work from it and much of the energy is wasted.
There are two ways to reduce knocking. First, you can mix the fuel and air more uniformly. In a non-uniform mixture, there may be small regions of gas that get hotter or are more susceptible to ignition than others. The fuel-injection technique used in all modern cars provides excellent mixing and also allows a car's computer to adjust the fuel–air mixture for complete combustion and minimal pollution. So unless a car is seriously out of tune, there isn't much room for improvement as far as mixture uniformity is concerned...
Second, you can use the most appropriate fuel. Not all fuels ignite at the same temperature, so you should select a fuel that is able to tolerate your car's compression process without igniting spontaneously. Fuels that are more difficult to ignite and more resistant to knocking are assigned higher “octane numbers.” Regular gasoline has an octane number of about 87 while premium has an octane number of about 93.
Since knocking sets the limit for compression ratio, it also sets the limit for efficiency in a gasoline engine. However, diesel engines avoid the knocking problem by:
separating the fuel and air during the compression stroke. The diesel engine has no spark plug to ignite the fuel. Instead, it compresses pure air with an extremely high compression ratio of perhaps 20 : 1 and then injects diesel fuel directly into the cylinder just as the power stroke begins. The fuel ignites spontaneously as it enters the hot, compressed air.
Because of its higher compression ratio, a diesel engine burns its fuel at a higher temperature than a standard gasoline engine and can therefore be more energy efficient. It effectively has a hotter “hot object” and can convert a larger fraction of heat into work. Unfortunately, a diesel engine is also harder to start than a gasoline engine and requires carefully timed fuel injection. Some gasoline or diesel engines combine fuel injection with a turbocharger.
A turbocharger is essentially a fan that pumps outdoor air into the cylinder during the induction stroke. By squeezing more fuel–air mixture into the cylinder, a turbocharger increases the engine's power output. The engine burns more fuel each power stroke and behaves like a larger engine. The fan of a turbocharger is powered by pressure in the engine's exhaust system. A nearly identical device called a supercharger is driven directly by the engine's output power.
The downside of a turbocharger, other than being expensive and wearing out rather quickly, is that it encourages knocking. As it squeezes air into the cylinder, it does work on that air and the air becomes hot. By providing cool, high-density air to the cylinders, the intercooler reduces the peak temperature of the compression stroke and avoids knocking.
Since the purpose of the engine is to extract work from the fuel–air mixture, it's important that each cylinder do more work than it consumes. Three of the strokes require the engine to do work on various gases, and only one of the strokes extracts work from the burned gas.
During the induction stroke, the engine does work drawing the fuel–air mixture into the cylinder. During the compression stroke, the engine does work compressing the fuel–air mixture. During the exhaust stroke, the engine does work squeezing the exhaust gas out of the cylinder. Fortunately, the work done on the engine by the hot burned gas during the power stroke more than makes up for the work the engine does during the other three strokes.
Still, the engine has to invest a great deal of energy into the cylinder before each power stroke. To provide this initial energy...
most four-stroke engines have four or more cylinders, timed so that there is always one cylinder going through the power stroke. The cylinder that is in the power stroke provides the work needed to carry the other cylinders through the three nonpower strokes, and there is plenty of work left over to propel the car itself.
While the pistons move back and forth, the engine needs a rotary motion to turn the car's wheels. The engine converts each piston's reciprocating motion into rotary motion by coupling that piston to a crankshaft with a connecting rod. The crankshaft is a thick steel bar, suspended in bearings, that has a series of pedal-like extensions, one for each cylinder. As the piston moves out of the cylinder during the power stroke, it pushes on the connecting rod and the connecting rod pushes on its crankshaft pedal. The connecting rod thus produces a torque on the crankshaft.
The crankshaft rotates in its bearings and transmits this torque out of the engine so that it can be used to propel the car. So, while each cylinder initially exerts a force, the crankshaft uses that force to produce a torque.

The spinning crankshaft conveys its rotary power to the car's transmission and from there the power moves on to the wheels. Overall, a significant portion of the heat flowing out of the burning fuel–air mixture is being converted into work and used to spin the car's wheels. Assisted by friction with the pavement, the wheels push the car forward and you cruise down the highway toward your destination.
Observations about
Air Conditioners 2. Natural Heat Flow
Air conditioners (Part 1)
The Evaporator (Part 1)
The Evaporator (Part 2)
The Compressor
The Condenser (Part 1)
The Condenser (Part 2)
Air Conditioner Overview
Internal Combustion Engine
Four Stroke Engine
Induction Stroke: fill cylinder with fuel & air
Induction Stroke
Compression Stroke
Power Stroke
Exhaust Stroke
Ignition System
Efficiency Limits
Knocking and Gasolines
Compressing a gas increases its temperature
Diesel Engine
Vehicle Pollution
Catalytic Converter
Manual Transmission
Automatic Transmission
Our perception of space is ultimately based on the need for:
forces, accelerations, and velocities to travel from one place to another.
natural resonance
the energy in an isolated object or system of objects causes it to perform a certain motion over and over again. Many objects in our world exhibit natural resonances, from tipping rocking chairs, to sloshing basins of water, to waving flagpoles, and those natural resonances usually involve motion about a stable equilibrium.
harmonic oscillators
the simplest and best understood mechanical system in nature. As a harmonic oscillator, the pendulum undergoes simple harmonic motion, a regular and predictable oscillation that makes it a superb timekeeper.
When the pendulum's center of gravity is directly below its pivot...
it's in a stable equilibrium. Its center of gravity is then as low as possible, so displacing it raises its gravitational potential energy and a restoring force begins pushing it back toward that equilibrium position. For geometrical reasons, this restoring force is almost exactly proportional to how far the pendulum is from equilibrium. As you displace the pendulum steadily from equilibrium, the restoring force on it also increases steadily.
When you release the displaced pendulum, its restoring force accelerates it back toward equilibrium. But instead of stopping, the pendulum swings back and forth about its equilibrium position in a repetitive motion called an oscillation. As it swings, its energy alternates between potential and kinetic forms. When it swings rapidly through its equilibrium position in the middle of a swing, its energy is all kinetic. When it stops momentarily at the end of a swing, its energy is all gravitational potential. This repetitive transformation of excess energy from one form to another is part of any oscillation and keeps the oscillator—the system experiencing the oscillation—moving back and forth until that excess energy is either converted into thermal energy or transferred elsewhere.
harmonic oscillator
But the pendulum isn't just any oscillator. Because its restoring force is proportional to its displacement from equilibrium, the pendulum is a harmonic oscillator—the simplest and best understood mechanical system in nature. As a harmonic oscillator, the pendulum undergoes simple harmonic motion, a regular and predictable oscillation that makes it a superb timekeeper.
The period of any harmonic oscillator:
the time it takes to complete one full cycle of its motion—depends only on how stiffly its restoring force pushes it back and forth and on how stubbornly its mass resists that back-and-forth motion.
the measure of how sharply the restoring force strengthens as the oscillator is displaced from equilibrium; stiff restoring forces are associated with firm or hard objects, while less stiff restoring forces are associated with soft objects. The stiffer the restoring force, the more forcefully it pushes the oscillator back and forth and the shorter the oscillator's period. On the other hand, the larger the oscillator's mass, the less it accelerates and the longer its period.
Its period doesn't depend on amplitude...
its furthest displacement from equilibrium. Whether that amplitude is large or small, the harmonic oscillator's period remains exactly the same. This insensitivity to amplitude is a consequence of its special restoring force, a restoring that is proportional to displacement from equilibrium. At larger amplitudes, the oscillator travels farther each cycle, but the forces accelerating it through that cycle are stronger as well. Overall, the harmonic oscillator completes a large cycle of motion just as quickly as it completes a small cycle of motion.
Actually, a pendulum is an unusual harmonic oscillator because its period is independent of its mass...
That's because increasing the pendulum's mass also increases its weight and therefore stiffens its restoring force. These two changes compensate for one another perfectly so that the pendulum's period is unchanged. A pendulum's period does, however, depend on its length and on gravity. When you reduce the pendulum's length—the distance from its pivot to its center of mass—you stiffen its restoring force and shorten its period.
While a pendulum maintains a steady beat, it's not a complete clock. Something must keep the pendulum swinging and use that swing to determine the time. A pendulum clock does both. It sustains the pendulum's motion with gentle pushes, and it uses that motion to advance its hands at a steady rate. The top of the pendulum has a two-pointed:
anchor that controls the rotation of a toothed wheel.This mechanism is called an escapement. A weighted cord wrapped around the toothed wheel's shaft exerts a torque on that wheel, so that the wheel would spin if the anchor weren't holding it in place. Each time the pendulum reaches the end of a swing, one point of the anchor releases the toothed wheel while the other point catches it.
The toothed wheel also keeps the pendulum moving by giving the anchor a tiny forward push each time the pendulum completes a swing. Since the anchor moves in the direction of the push...
the wheel does work on the anchor and pendulum, and replaces energy lost to friction and air resistance. This energy comes from the weighted cord, which releases gravitational potential energy as its weight descends. When you wind the clock, you rewind this cord around the shaft, lifting the weight and replenishing its potential energy.
While these pushes from the toothed wheel can keep even the clumsiest pendulum swinging, a clock works best when its pendulum swings with almost perfect freedom. That's because any outside force...
even the push from the toothed wheel—will influence the pendulum's period. The most accurate timekeepers are those that can oscillate without any assistance or energy replacement for thousands or millions of cycles. These precision timekeepers need only the slightest pushes to keep them moving and thus have extremely precise periods. That's why a good pendulum clock uses an aerodynamic pendulum and low-friction bearings.
Finally, the clock must keep the oscillation amplitude of its pendulum relatively constant. From a practical perspective, drastic changes in that amplitude will make the toothed wheel turn erratically. But there is a more fundamental reason to keep the pendulum's amplitude steady: it's not really a perfect harmonic oscillator. If you displace the pendulum too far, it becomes an anharmonic oscillator...
its restoring force ceases to be proportional to its displacement from equilibrium, and its period begins to depend on its amplitude. Since a change in period would spoil the clock's accuracy, the pendulum's amplitude must be kept small and steady. That way, the amplitude has almost no effect on the pendulum's period.
A balance ring resembles a tiny metal bicycle wheel, supported at:
its center of mass/gravity by an axle and a pair of bearings (Fig. 9.1.6). Any friction in the bearings is exerted so close to the ring's axis of rotation that it produces little torque and the ring turns extremely easily. Moreover, the ring pivots about its own center of gravity so that its weight produces no torque on it.
The only thing exerting a torque on the balance ring is a tiny coil spring. One end of this spring is attached to...
the ring while the other is fixed to the body of the clock. When the spring is undistorted, it exerts no torque on the ring and the ring is in equilibrium. But if you rotate the ring either way, torque from the distorted spring will act to restore it to its equilibrium orientation. Since this restoring torque is proportional to the ring's rotation away from a stable equilibrium, the balance ring and coil spring form a harmonic oscillator!
Because of the rotational character of this harmonic oscillator, its period depends on the torsional stiffness of the coil spring—how rapidly the spring's torque increases as you twist it—and on the balance ring's rotational mass.
Since the balance ring's period doesn't depend on the amplitude of its motion, it keeps excellent time. And because gravity exerts no torque on the balance ring, this timekeeper works anywhere and in any orientation.
The rest of a balance clock is similar to a pendulum clock...
As the balance ring rocks back and forth, it tips a lever that controls the rotation of a toothed wheel. An anchor attached to the lever allows the toothed wheel to advance one tooth for each complete cycle of the balance ring's motion. Gears connect the toothed wheel to the clock's hands, which slowly advance as the wheel turns.
Because the balance clock is portable, it can't draw energy from a weighted cord. Instead...
it has a main spring that exerts a torque on the toothed wheel. This main spring is a coil of elastic metal that stores energy when you wind the clock. Its energy keeps the balance ring rocking steadily back and forth and also turns the clock's hands. Since the main spring unwinds as the toothed wheel turns, the clock occasionally needs winding.
The potential accuracy of pendulum and balance clocks is limited by friction, air resistance, and thermal expansion to about ten seconds per year. To do better, a clock's timekeeper must avoid these mechanical shortcomings. That's why so many modern clocks use quartz oscillators as their timekeepers...
A quartz oscillator is made from a single crystal of quartz, the same mineral found in most white sand. Like many hard and brittle objects, a quartz crystal oscillates strongly after being struck. In fact, it's a harmonic oscillator because it acts like a spring with a block at each end (Fig. 9.1.8a,b). The two blocks oscillate in and out symmetrically about their combined center of mass, with a period determined only by the blocks' masses and the spring's stiffness. In a quartz crystal, the spring is the crystal itself and the blocks are its two halves. Since the forces on the blocks are proportional to their displacements from equilibrium, they're harmonic oscillators.
Because of its exceptional hardness, a quartz crystal's restoring force is extremely stiff. Even a tiny distortion leads to a huge restoring force. Since the period of a harmonic oscillator decreases as its spring becomes stiffer, a typical quartz oscillator has an extremely short period. Its motion is usually called a vibration...
rather than an oscillation because vibration implies a fast oscillation in a mechanical system. Oscillation itself is a more general term for any repetitive process and can even apply to such nonmechanical processes as electric or thermal oscillations.
Because of its rapid vibration, a quartz oscillator's period is a small fraction of a second. We normally characterize such a fast oscillator by its frequency—the number of cycles it completes in a certain amount of time. The SI unit of frequency is the cycle-per-second...
also called the hertz (abbreviated Hz) after German physicist Heinrich Rudolph Hertz. Period and frequency are reciprocals of one another (period equals 1/frequency and vice versa) so that an oscillator with a period of 0.001 s has a frequency of 1000 Hz.
Because the vibrating crystal isn't sliding across anything or moving quickly through the air, it loses energy slowly and vibrates for a long, long time. And because quartz's coefficient of thermal expansion is extremely small, the crystal's period is nearly independent of its temperature. With its exceptionally steady period, a quartz oscillator can serve as the timekeeper for a highly accurate clock, one that loses or gains less than a tenth of a second per year. Of course, a quartz crystal isn't a complete clock.
Like the pendulum and balance, it needs something to keep it vibrating and use that vibration to determine the time. While these tasks could conceivably be done mechanically, quartz clocks are normally electronic. There are two reasons for this choice. First, the crystal's vibrations are too fast and too small for most mechanical devices to follow. Second, a quartz crystal is intrinsically electronic itself; it responds mechanically to electrical stress and electrically to mechanical stress. Because of this coupling between its mechanical and electrical behaviors, crystalline quartz is known as a piezoelectric material and is ideal for electronic clocks.
The clock's circuitry uses electrical stresses to keep the quartz crystal vibrating...
Just as carefully timed pushes keep a child swinging endlessly on a playground swing, carefully timed electrical stresses keep the quartz crystal vibrating endlessly in its holder. Because the crystal loses so little energy with each vibration, only a tiny amount of work is required each cycle to maintain its vibration.
The clock also detects the crystal's vibrations electrically...
Each time its halves move in or out, the crystal experiences mechanical stress and emits a pulse of electricity. These pulses may control an electric motor that advances clock hands or may serve as input to an electronic chip that measures time by counting the pulses.
The quartz crystals used in clocks and watches are carefully cut and polished to vibrate at specific frequencies. The thinner the crystal, the faster it vibrates—less mass and a stiffer restoring force. In effect, these crystals are tuned like musical instruments to match the requirements of their clocks.
While most tiny quartz crystals vibrate millions of times each second...
common watch crystals vibrate at 215 Hz or 32,768 Hz. This low frequency prolongs a watch's battery life because counting each pulse consumes some of the battery's energy. To make a small crystal vibrate this slowly, the manufacturer cuts away most of the center of the crystal to weaken its restoring force and slow its oscillations. The resulting quartz “tuning fork” oscillator is carefully metalized to permit the watch to interact with it electrically, and it's then tuned to exactly 32,768 Hz by burning away some of the metal mass with a laser beam.
To understand how instruments work, we'll need to know a bit more about sound and music. In air, sound consists of:
density waves—patterns of compressions and rarefactions that travel outward rapidly from their source. When a sound passes by, the air pressure in your ear fluctuates up and down about normal atmospheric pressure. Even when these fluctuations have amplitudes less than a millionth of atmospheric pressure, you hear them as sound.
When the fluctuations are repetitive, you hear a tone with a pitch equal to the fluctuation's frequency. Pitch is:
the frequency of a sound. A bass singer's pitch range extends from 80 Hz to 300 Hz, while that of a soprano singer extends from 300 Hz to 1100 Hz. Musical instruments can produce tones over a much wider range of pitches, but we can only hear those between about 30 Hz and 20,000 Hz, and that range narrows as we get older.
Most music is constructed around intervals...
the frequency ratio between two different tones. This ratio is found by dividing one tone's frequency by that of the other. Our hearing is particularly sensitive to intervals, with pairs of tones at equal intervals sounding quite similar to one another. For example, a pair of tones at 440 Hz and 660 Hz sounds similar to a pair at 330 Hz and 495 Hz because they both have the interval 3/2.
The interval 3/2 is pleasing to most ears and is common in Western music, where it's called a fifth. A fifth is the interval between the two “twinkles” at the beginning of “Twinkle, Twinkle, Little Star.” The most important interval in virtually all music is 2/1 or an:
octave. Tones that differ by a factor of 2 in frequency sound so similar to our ears that we often think of them as being the same. When men and women sing together “in unison,” they often sing an octave or two apart and the differences in the tones, always factors of 2 or 4 in frequency, are only barely noticeable. The octave is so important that it structures the entire range of audible pitches. Most of the subtle interplay of tones in music occurs in intervals of less than an octave, less than a factor of 2 in frequency. Thus most traditions build their music around the intervals that lie within a single octave, such as 5/4 and 3/2. They pick a particular standard pitch and then assign notes at specific intervals from this standard pitch. This arrangement repeats at octaves above and below the standard pitch to create a complete scale of notes.
The scale used in Western music is constructed around a note called A4 or Concert A which has a standard pitch of 440 Hz. Actually, Western music is built around 12 notes and 11 intervals that lie within...
a single octave. Five more intervals account for five additional notes, Bb4, C5, D#5, F5, and G5. It's also not quite true that every note is based exclusively on its interval from A4. While A4 remains at 440 Hz, the pitches of the other 11 notes have been modified slightly so that they're at interesting and pleasing intervals from one another as well as from A4. This adjustment of the pitches led to the well-tempered scale that has been the basis for Western music for the last several centuries.
The tones produced by a violin begin as vibrations in its strings. But these strings are limp and shapeless on their own and rely on the violin's rigid body and neck for structure. The violin subjects its strings to tension...
outward forces that act to stretch it—and this tension gives each string an equilibrium shape: a straight line.
The net forces on its pieces are restoring forces because they act to straighten the string. If you distort the string and release it, these restoring forces will cause the string to vibrate about its straight equilibrium shape in a natural resonance. But the string's restoring forces are special: the more you curve the string, the stronger the restoring forces on its pieces become. In fact, the restoring forces are:
springlike forces—they increase in proportion to the string's distortion—so the string is a form of harmonic oscillator!
Actually, the string is much more complicated than a pendulum or a balance ring.
It can bend and vibrate in many distinct modes:
or basic patterns of distortion, each with its own period of vibration. Nonetheless, the string retains the most important feature of a harmonic oscillator: the period of each vibrational mode is independent of its amplitude. Thus a violin string's pitch doesn't depend on how hard it's vibrating. Think how tricky it would be to play a violin if its pitch depended on its volume!
A violin string has a simplest vibration: its fundamental vibrational mode.
In this mode, the entire string arcs alternately one way then the other (Fig. 9.2.3). Its kinetic energy peaks as it rushes through its straight equilibrium shape and its potential energy (elastic potential energy in the string) peaks as it stops to turn around. The string's midpoint travels the farthest (the vibrational antinode) while its ends remain fixed (the vibrational nodes). At each moment its shape is the gradual curve of the trigonometric sine function.
In this fundamental mode, the violin string behaves as a single harmonic oscillator. As with any harmonic oscillator, its vibrational period depends only on the stiffness of its restoring forces and on its inertia. Stiffening the violin string or reducing its mass...
both quicken its fundamental vibration and increase its fundamental pitch. A violin has four strings, each with its own stiffness and mass and therefore its own fundamental pitch.
You tune a violin by adjusting the tension in its strings, using pegs in its neck and tension adjusters on the tailpiece. Tightening the string stiffens it by...
increasing both the outward forces on its pieces and the net forces they experience during a distortion. Since temperature and time can alter a string's tension, you should always tune your violin just before a concert.
string's fundamental pitch also depends on its length. Shortening the string both stiffens it and reduces its mass, so its pitch increases. That stiffening occurs because a shorter string curves more sharply when it's displaced from equilibrium and therefore subjects its pieces to larger net forces. This dependence on length allows you to raise a string's pitch by pressing it against the fingerboard in the violin's neck and effectively shortening it. If the arc of a string vibrating in its fundamental mode reminds you of a wave, that's because it is one. It's a mechanical wave:
the natural motions of an extended object about its stable equilibrium shape or situation. An extended object is one like a string, stick, or lake surface that has many parts that move with limited independence. Since its parts influence one another, an extended object with a stable equilibrium exhibits fascinating natural motions that involve many parts moving at once; it exhibits mechanical waves.
With its innumerable linked pieces and its stable equilibrium shape, the violin string exhibits such waves. And the string's fundamental mode is a particularly simple wave, a standing wave:
a wave in which all the nodes and antinodes remain in place. A standing wave's basic shape doesn't change with time, it merely scales up and down rhythmically at a particular frequency and amplitude—its peak extent of motion. Most importantly, the standing wave doesn't travel along the string.
Although this wave extends along the string, its associated oscillation is perpendicular to the string and therefore perpendicular to the wave itself. A wave in which the underlying oscillation is perpendicular to the wave itself is called a:
transverse wave. Waves on strings, drums, and the surface of water are all transverse waves.
The fundamental vibrational mode isn't the only way in which a violin string can vibrate. The string also has higher-order vibrational modes...
in which the string vibrates as a chain of shorter strings arcing in alternate directions. Each of these higher-order vibrational modes is another standing wave, with a fixed shape that scales up and down rhythmically at its own frequency and amplitude.
For example, the string can vibrate as two half-strings arcing in opposite directions and separated by a motionless vibrational node. In this mode, the violin string not only vibrates as half-strings, it has the pitch of half-strings as well. Remarkably, that half-string pitch is exactly twice the whole-string (i.e., fundamental) pitch! In general, a string's vibrational frequency is inversely proportional to its length, so halving its length doubles its frequency. Frequencies that are integer multiples of the fundamental pitch are called
frequency is inversely proportional to its length, so halving its length doubles its frequency. Frequencies that are integer multiples of the fundamental pitch are called harmonics, so this half-string vibration occurs at the second harmonic pitch and is called the second harmonic mode. A violin string can also vibrate as three third-strings, with a frequency that's three times the fundamental. The interval between this third harmonic pitch and the fundamental pitch is an octave and a fifth (2/1 times 3/2). Overall, the fundamental and its second and third harmonics sound very pleasant together.
While the violin string can vibrate in even higher harmonics, what's more important is that the string often vibrates in more than one mode at the same time. For example, a violin string vibrating in its fundamental mode can also vibrate in its second harmonic and emit two tones at once. Harmonics are important because bowing a violin excites many of its vibrational modes. The violin's sound is thus a rich mixture of the fundamental tone and the harmonics. Known as timbre
this mixture of tones is characteristic of a violin, which is why an instrument producing a different mixture doesn't sound like a violin.
When a violin string is vibrating in several modes at once, its shape and motion are complicated. The individual standing waves add on top of one another, a process known as:
superposition. Each vibrational mode has its own amplitude and therefore its own volume contribution to the string's timbre. While these individual waves coexist beautifully on the string, with virtually no effect on one another, the string's overall distorted shape is now the superposition of the individual waveshapes. Not only is that overall shape quite complicated, it actually changes substantially with time. That's because the different harmonic waves vibrate at different frequencies and their superposition changes as they change. The string's overall wave is not a standing wave and its features can even move along the string!
You play a violin by drawing a bow across its strings. The bow consists of horsehair, pulled taut by a wooden stick. Horsehair is rough and exerts frictional forces on the strings as it moves across them. But most importantly, horsehair exerts much larger static frictional forces than sliding ones. As the bow hairs rub across a string, they grab the string and push it forward with static friction. Eventually...
the string's restoring force overpowers static friction, and the string suddenly starts sliding backward across the hairs. Because the hairs exert little sliding friction, the string completes half a vibrational cycle with ease. But as it stops to reverse direction, the hairs grab the string again and begin pushing it forward. This process repeats over and over.
Each time the bow pushes the string forward, it does work on the string and adds energy to the string's vibrational modes. This process is an example of resonant energy transfer:
In which a modest force doing work in synchrony with a natural resonance can transfer a large amount of energy to that resonance. Just as gentle, carefully timed pushes can get a child swinging high on a playground swing, so gentle, carefully timed pushes from a bow can get a string vibrating vigorously on a violin.
Similar pushes can cause other objects to vibrate strongly, notably a crystal wineglass and the Tacoma Narrows Bridge near Seattle. The wineglass's response to a certain tone is also an example of sympathetic vibration...
the transfer of vibrational energy between two systems that share a common vibrational frequency.
The amount of energy the bow adds to each vibrational mode depends on where it crosses the violin string. When you bow the string at the usual position, you produce a strong fundamental vibration and a moderate amount of each harmonic. Bowing the string nearer its middle reduces the string's curvature, weakening its:
harmonic vibrations and giving it a more mellow sound. Bowing the string nearer its end increases the string's curvature, strengthening its harmonic vibrations and giving it a brighter sound.
The sound of a plucked violin string also depends on harmonic content and thus on where that string is plucked. But this sound is quite different from that of a bowed string. The difference lies in the sound's envelope:
the way the sound evolves with time. This envelope can be viewed as having three time periods: an initial attack, an intermediate sustain, and a final decay. The envelope of a plucked string is an abrupt attack followed immediately by a gradual decay. In contrast, the envelope of a bowed string is a gradual attack, a steady sustain, and then a gradual decay. We learn to recognize individual instruments not only by their harmonic content but also by their sound envelopes.
Like a violin, a pipe organ uses vibrations to create sound. However, its vibrations take place in the air itself. An organ pipe is essentially a hollow cylinder, open at each end and filled with air. Because that air is isolated, its pressure can fluctuate up and down relative to atmospheric pressure and it can exhibit natural resonances. In its fundamental vibrational mode, air moves alternately...
toward and away from the pipe's center, like two blocks on a spring. As air moves toward the pipe's center, the density there rises and a pressure imbalance develops. Since the pressure at the pipe's center is higher than at its ends, air accelerates away from the center. The air eventually stops moving inward and begins to move outward. As air moves away from the pipe's center, the density there drops and a reversed pressure imbalance occurs. Since the pressure at the pipe's center is lower than at its ends, air now accelerates toward the center. It eventually stops moving outward and begins to move inward, and the cycle repeats. The air's kinetic energy peaks each time it rushes through that equilibrium and its potential energy (pressure potential energy in the air) peaks each time it stops to turn around.
This air is vibrating about a stable equilibrium of uniform atmospheric density and pressure, and is clearly experiencing restoring forces. It should come as no surprise that those restoring forces are springlike and that the air column is yet another harmonic oscillator. As such, its vibrational frequency depends only on the stiffness of its restoring forces and on its inertia. Stiffening the air column or reducing its mass both quicken its vibration and increase its pitch. These characteristics depend on:
the length of the organ pipe. A shorter pipe not only holds less air mass than a longer pipe, it also offers stiffer opposition to any movements of air in and out of that pipe. With less room in the shorter pipe, the pressure inside it rises and falls more abruptly, leading to stiffer restoring forces on the moving air. Together, these effects make the air in a shorter pipe vibrate faster than that in a longer pipe. In general, an organ pipe's vibrational frequency is inversely proportional to its length.
Unfortunately, the mass of vibrating air in a pipe also increases with the air's average density, so that even a modest change in temperature or weather will alter the pipe's pitch. Fortunately, all of the pipes shift together...
so that an organ continues to sound in tune. Nonetheless, this shift may be noticeable when the organ is part of an orchestra. As you may suspect, the fundamental vibrational mode of air in the organ pipe is another standing wave. Air in the pipe is an extended object with a stable equilibrium and the disturbance associated with its fundamental vibrational mode has a basic shape that doesn't change with time; it merely scales up and down rhythmically.
However, the shape of the wave in the pipe's air now has to do with back-and-forth compressions and rarefaction, not with side-to-side displacements as it did in the violin string. In fact, all of the wave's associated oscillation is along the pipe and therefore along the wave itself. A wave in which the underlying oscillation is parallel to the wave itself is called a:
longitudinal wave. Waves in the air, including those inside organ pipes and other wind instruments and sound waves in the open air, are all longitudinal waves.
The organ uses resonant energy transfer to make the air in a pipe vibrate. It starts this transfer by:
blowing air across the pipe's lower opening, although for practical reasons that lower opening is usually found on the pipe's side. As the air flows across the opening, it's easily deflected and tends to follow any air that's already moving into or out of the pipe. If the air inside the pipe is vibrating, the new air will follow it in perfect synchrony and strengthen the vibration.
This following process is so effective at enhancing vibrations that it can even initiate a vibration from the random noise that's always present in a pipe. That's how the sound starts when the organ's pump first blows air across the pipe. Once the vibration has started, it grows quickly in amplitude until energy leaves the pipe as sound and heat as quickly as it arrives via compressed air. The more air the organ blows across the pipe each second...
the more power it delivers to the pipe and the louder the vibration. Like a violin string, an organ pipe can support more than one mode of vibration. In its fundamental vibrational mode, the pipe's entire column of air vibrates together. In the higher-order vibrational modes, this air column vibrates as a chain of shorter air columns moving in alternate directions. If the pipe has a constant width, these vibrations occur at harmonics of the fundamental. When the air column vibrates as two half-columns, its pitch is exactly twice that of the fundamental mode. When it vibrates as three third-columns, its pitch is exactly three times that of the fundamental.
But the air column inside a pipe can vibrate in more than one mode simultaneously. As with a violin string, the standing waves superpose and the fundamental and harmonic tones are produced together. The shape of the organ pipe and the place where air is blown across it determine the pipe's harmonic content and thus its timbre. Different pipes can imitate different instruments. To sound like a flute...
the pipe should emit mostly the fundamental tone and keep the harmonics fairly quiet. To sound like a clarinet, its harmonics should be much louder. An organ pipe's volume always builds slowly during the attack, so it can't pretend to be a plucked string. However, a clever designer can make the organ imitate a surprising range of instruments.
After examining violin strings and organ pipes, it might seem that drums offer little new. But while a drumhead is yet another extended object with a stable equilibrium and springlike restoring forces, its overtone vibrations have an important difference: they aren't harmonics.
Violin strings and organ pipes are effectively one-dimensional objects, dividing easily into half-objects or third-objects that then vibrate at second or third harmonic pitches. Together with the many other one-dimensional instruments in an orchestra or band, they blend seamlessly when they're playing the same fundamental pitch because they share the same harmonics.
But because a drumhead is effectively two-dimensional, it doesn't divide easily into pieces that resemble the entire drumhead. As a result, the pitches of its overtone vibrations have no simple relationship to its fundamental pitch. A kettledrum or timpani stands out relative to other instruments in part because of the unique overtone pitches. Each vibrational mode is a standing wave...
but with vibrational nodes that are curves or lines rather than points. The fundamental mode (a) has only one node on its outer edge, while the overtone modes have additional nodes within the surface. In each vibrational mode, these nodes remain motionless as the rest of the surface vibrates up and down, its peaks and valleys interchanging alternately. The pitches of the overtone vibrations are indicated relative to that of the fundamental vibration.
Because striking a drumhead causes it to vibrate in several modes at once, the drum emits several pitches simultaneously. The amplitude of each mode, and consequently its volume, depends not only on how hard you hit the drumhead, but also:
on where you hit it. If you hit it at its center, it vibrates primarily in circular modes like (a) and (d). If you hit it nearer its edge, it also vibrates in noncircular modes. A timpani sounds most musical when it's struck off-center in such a way that the amplitude of its fundamental vibrational mode is nearly zero and its overtones, particularly (b), dominate its sound. That's because the fundamental vibrational mode emits sound so well that its vibrational energy dissipates before it can produce a discernible tone. Unless all you want is a loud “thump,” you must hit the timpani off-center so that its long-lived overtone vibrations receive most of the energy and emit most of the sound. The dominant pitch of a properly played timpani is that of its first overtone vibration and it is tuned with that pitch in mind. In truth, the pitches shown neglect the effects of air's inertia on the drumhead's vibrations. Since air adds inertia to the drumhead, it lowers the pitches of all the vibrational modes, some more than others. Because of air's influence on pitch, a drum must be tuned to accommodate changes in temperature and weather.
Neglecting gravity, air is in a stable equilibrium when its density is uniform. If we disturb it from equilibrium, the resulting pressure imbalances will provide springlike restoring forces. These forces, together with air's inertia, lead to rhythmic vibrations:
the vibrations of harmonic oscillators. In open air, the most basic vibrations are waves that move steadily in a particular direction and are therefore called traveling waves. Like the standing waves inside an organ pipe, these traveling waves in open air are longitudinal—air vibrates along the same direction as the sound wave travels.
As it moves through the open air, a basic traveling sound wave consists of an alternating pattern of high density regions we'll call crests and low density regions we'll call troughs...
While those names will seem more appropriate when we examine water surface waves in the next section, it's customary to refer to the alternating highs and lows of any wave as crests and troughs, respectively. Whether a wave is standing or traveling, the shortest distance between two adjacent crests is known as the wavelength.
While a standing wave's crests and troughs merely flip back and forth in place, crests becoming troughs and troughs becoming crests, a traveling wave's crests and troughs move steadily in a particular direction at a particular speed. That speed and direction of travel together constitute the traveling wave's...
traveling wave's wave velocity. Since a crest moves one wavelength per vibration cycle and frequency is the number of vibration cycles per second, the speed at which the crest moves is the product of the wavelength times the frequency.
Remarkably enough, all sound waves travel at the same speed through air, regardless of wavelength or frequency. That's because a sound's wavelength is always inversely proportional to its frequency. We saw this same inverse relationship for the standing waves in organ pipes: if you double the length of a pipe, and therefore double the wavelength of its fundamental vibrational mode, you halve the frequency of that vibration. Even when it's not confined by a pipe, vibrating air has a wavelength that's inversely proportional to the frequency of that vibration. Because of this extraordinary inverse relationship between a traveling sound wave's wavelength and its frequency, Eq. 9.2.1 yields the same wave speed for any sound wave. Known as the speed of sound
in air, it's about 331 m/s (1086 ft/s) in standard conditions at sea level (0 °C, 101,325 Pa pressure). While that's fast, there is still a noticeable delay between when a percussionist strikes the cymbals and when you hear them from across the concert hall. Fortunately, because the speed of sound doesn't depend on frequency, when the entire orchestra plays in unison you hear all its different pitches simultaneously.
This discussion of sound assumes that the instruments and listener maintain a constant separation, as they usually do at an orchestra concert. But when a marching band dashes toward or away from the listener, something odd happens: the listener hears its music shifted up or down in pitch. Known as the Doppler effect:
this frequency shift occurs because the listener encounters sound wave crests at a rate that's different from that at which those crests were created. If an instrument and the listener are approaching one another, the listener encounters the crests at an increased rate and the pitch increases. If the two are separating from one another, the listener encounters the crests at a decreased rate and the pitch decreases. Fortunately, the Doppler effect is subtle at speeds that are small compared to the speed of sound, so you can listen to parades without them sounding flat or sharp.
Anything that disturbs air's otherwise uniform density can produce traveling sound waves. Instruments emit sound by compressing and rarefying the nearby air in synch with their own vibrations. How they accomplish this task differs from instrument to instrument, so we'll have to look at them individually. As we'll see, some instruments find it easier to produce sound than others.
A drum produces sound when its vibrating drumhead alternately compresses and rarefies the nearby air. As portions of that drumhead rise and fall, they upset the air's uniform density and thereby produce sound waves. But whenever it can...
air simply flows silently out of the drumhead's way, leading to smaller density fluctuations and less intense sound. For example, when the drumhead is experiencing one of the five overtone vibrations shown in Fig. 9.2.9, air flows away from each rising peak in the undulating surface and toward each falling valley. The overtone vibrations still manage to produce sound, but it's less intense and the vibrational energy in the drumhead transforms relatively slowly into sound energy.
Air's partial success in dodging the drumhead's overtone vibrations allows those overtones to complete many vibrational cycles before running out of vibrational energy. Their vibrations are therefore long-lived and have distinct pitches. In contrast, air has difficulty dodging the drumhead's fundamental vibrational mode, which alternately compresses and rarefies the air so effectively that it transfers all of its vibrational energy to the air in just a few cycles. That's why the fundamental vibrational mode produces:
an intense and nearly pitchless “thump” sound.
If air can dodge a vibrating surface, it can certainly dodge a vibrating string. Little of a violin's sound comes directly from its vibrating strings; the air simply skirts around them. Instead, the violin creates sound with its top plate or belly. The strings transfer their vibrational motions to the belly and the belly pushes on the air to create sound.
Most of this vibrational energy flows into the belly through the violin's bridge:
which holds the strings away from the violin's body (Fig. 9.2.13). Beneath the G3 string side of the bridge is the bass bar, a long wooden strip that stiffens the belly. Beneath the E5 side of the bridge is the sound post, a shaft that extends from the violin's belly to its back.
As a bowed string vibrates across the violin's belly, it exerts a torque on the bridge about the sound post. The bridge rotates back and forth, causing the bass bar and belly to move in and out. The belly's motion produces most of the violin's sound. Some of this sound comes directly from the belly's outer surface, and the rest comes from its inner surface and must emerge through its f-shaped holes. An organ pipe doesn't have to produce sound because:
that sound already exists. In effect, the pipe's vibrating column of air is a standing sound wave that gradually leaks out of the pipe as a traveling one. Trapped sound is escaping from its container.
This conversion of a standing wave into a traveling wave isn't so remarkable because the two types of waves are closely related. The pipe's standing wave can be thought of as a reflected traveling wave, a traveling wave that's bouncing back and forth between the two ends of the pipe. Because of the reflections, the traveling wave is superposed with itself heading in the opposite direction and the sum of two equal but oppositely directed traveling waves is a standing wave! The fact that sound reflects from the open end of an organ pipe is rather surprising.
If that end were closed, you'd probably expect a reflection. After all, sound echos from cliffs and other rigid surfaces. But sound partially reflects from a surprising range of other transitions, including the transition from inside a pipe to outside it. If you don't believe that, clap your hands inside a long pipe and listen for the decaying echos. The reflections at the organ pipe's open ends aren't perfect, so the trapped sound wave gradually leaks out and becomes the sound you hear. This process of letting a standing sound wave emerge slowly as a traveling wave is typical of woodwind and brass instruments. The reflection at an open pipe end depends on the shape of that end. Flaring it into the horn shape common in brass instruments reduces the reflection and eases the transition from standing wave to traveling wave. That's why horns project sound so well.
The differences between the moon's gravity at particular locations on earth and its average strength for the entire earth give rise to tidal forces:
residual gravitational forces that act to displace those locations relative to the earth as a whole. The near side of the earth is pulled toward the moon more strongly than average so it experiences a tidal force toward the moon. The far side of the earth is pulled toward the moon less strongly than average so it experiences a tidal force away from the moon.
If the earth were less rigid, these tidal forces would stretch it into an egg shape. The near side of the earth would bulge outward toward the moon, while the far side of the earth would bulge outward away from the moon. But while the earth itself is too stiff to deform much, the oceans are not and they bulge outward in response to the tidal forces. Two tidal bulges appear:
one closest to the moon and one farthest from the moon. A beach located in one of these tidal bulges experiences high tide, while one in the ring of ocean between the bulges experiences low tide.
As the earth rotates, the locations of the two tidal bulges move westward around the equator. Since a particular beach experiences high tide whenever it's closest to or farthest from the moon, the full cycle from high to low to high tide occurs about once every 12 hours and 25 minutes. The extra 25 minutes reflects the fact that the moon isn't stationary; it orbits the earth every 27.3 days and thus passes overhead once every 24 hours and 50 minutes, rather than every 24 hours.
But the moon isn't the only source of tidal forces on the earth's oceans. Although the sun is much farther away than the moon, it's so massive that the tidal forces it exerts are almost half as large as those exerted by the moon. The sun's principal effect is to increase or decrease the strength of the tides caused by the moon (Fig. 9.3.3). When the moon and the sun are aligned with one another, their tidal forces add together and produce:
extra large tidal bulges. When the moon and the sun are at right angles to one another, their tidal forces partially cancel and produce tidal bulges that are unusually small.
Twice each lunar month, the time it takes for the moon to orbit the earth, the tides are particularly strong. These spring tides occur whenever the moon and sun are aligned with one another (full moon and new moon). Twice each lunar month the tides are particularly weak. These neap tides occur:
whenever the moon and sun are at right angles to one another (half moon). Because of this interplay between lunar and solar tidal effects, the cycle of tides varies slightly from day to day. While the average cycle is 12 hours and 25 minutes, it fluctuates over a lunar month. Moreover, the exact moment of high or low tide at a particular location is influenced by water's inertia, the earth's rotation, and the environment through which water must flow to form the tidal bulge. That's why shore areas often publish tables of the local tides.