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227 Cards in this Set
- Front
- Back
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Capacitance |
C=kE0A/d
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P-conduction |
changeQ/t = -kA (delta T/delta x) |
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Work/ Energy |
W= P (dV) = (F/A) (A) (dx)= F (dx) PdV= F/A Adx |
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isobaric |
volume changes pressure constant |
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isochoric |
P changes V constant W=0 |
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isothermal |
P changes V changes T constant Q=W |
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Adiabatic |
gases expanding/contracting so fast that there's NO heat exchange Q=0 delta E(int) = -W(by) |
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open system |
can exchange matter and heat |
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closed system |
only heat exchange |
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isolated system |
neither heat or matter can be exchanged (adiabatic) |
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P gauge |
P gauge = pdg =Fg (fluid) /A =pVg/A |
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Apparent Weight |
Fn = Fg - Fb |
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floating |
(p obj/p fluid) = (v sub/ v obj) |
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incompressible fluids flow rate is |
constant A1V1 = A2V2 f = Av
A proportional to 1/V |
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Bernoulli's Equ. |
P1 + (1/2)pv1^2 + pgy1 = P2 + (1/2)pv2^2 + pgy2 if v2>v1; y1=y2; P2 < P1 |
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Bernoulli's Equ only applies if |
1. fluid is incompressible (density constant) 2. negligible viscosity (thickness) 3. flow is laminar 4. flow rate constant |
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conduction |
transfer of heat by direct contact diff materials conduct heat at diff rates |
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convection |
heat transfer due to motion of fluid |
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radiation |
heat transfer due to electromagnetic |
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Internal Energy |
E(int) = Qin - Wby |
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Hooke's law |
F=-kx force of a spring, x=displacement negative slope= resulting force and displacement have opposite directions |
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Boyle's Law |
PV=k |
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KE |
= 1/2 mv^2 |
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Fgrav |
Gm1m2/ r^2 |
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Coulomb's Law |
F(electrostatic)= kq1q2/ r2 |
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momentum |
p= mv |
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Pressure |
P= F/A |
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Power |
P= E/ t or W/t (Fdcos(theta)/ t) P= Fv if v is constant and parallel P= VI (voltage x current) P= I^2 R |
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Frequency[2] |
f= oscillations/ t f= 1/T (period) |
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Radioactivity Activity |
= disintegrations/ t |
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Electric Potential(V) |
V= Energy/Charge V= kQ/r voltage = dV = volts associated with position. how much work per unit charge |
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Elect. Current |
I= Charge/t I= dQ/dt |
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Elect. Resistance [2] |
R= Potential/ Current or Voltage/ Current R= V/I |
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Capacitance |
C= Charge/ Electric Potential C = Q/V |
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Voltage |
V= IR |
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Electric Field (E) [2] |
E= F/Q (Force/ Charge) E= kQ/r^2 |
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Magnetic Field |
B= F/ Qv (Force/ charge x velocity) |
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Magnetic Flux |
F= BA (magnetic field x Area) |
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1000 L |
= 1m^3 |
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1mL |
= 1cc |
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?torr= ?mm Hg= ?atm |
760 torr= 760 mm Hg= 1 atm |
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1 atm= |
10^5 Pa |
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density of water |
1g/mL 1000 kg/m^3 |
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charge on electron 1eV |
-1.6 x 10^-19 C 1.6 x 10^-19 J |
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torque |
t=Frsin(theta) tnet = I a (inertia * rotational acceleration) |
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F circular motion |
mv2/r |
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centripetal acceleration |
v2/r towards center of circle |
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when work = 0 |
F is perpendicular to d |
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Work when F is constant |
Fdcos(theta) |
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Work and KE |
W= dKE |
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PE and ME |
PE = mgh = Fgd |
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when work done by system in same direction as field force |
W(+ ) and dPE (-) |
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ME |
ME = PE + KE conservative force dME= 0 when no non-conservative forces |
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Mechanical Advantage |
F resitance/ F effort output/input always >1 |
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Efficiancy |
W output/ E input |
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centripetal Force |
F= mv2/r |
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Fgrav = Fc |
GMm/r^2 = mv^2/r v= sqrt(GM/r) |
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any object orbiting at the same distance from the earth as the moon...? |
must move at same speed |
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What is Electric Potential Energy? |
Electric potential energy is the energy that is needed to move a charge against an electric field. You need more energy to move a charge further in the electric field, but also more energy to move it through a stronger electric field. amount of work applied PEe= qV EP increases when you get closer to like charge EP increases when you get farther from opposite charge |
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Resistance in terms of resistivity |
R= pL/A p=resistivity |
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time (t) |
= Sqrt(2d/g) |
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translational speed (v) |
v= sqrt(GM/r) |
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equilibrium |
zero acceleration both translational and rotational acceleration = 0 |
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static equilibrium |
zero acceleration and velocity= 0 |
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translational equlibrium |
if forces cancel (Fnet=0) then translational acceleration = 0 |
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rotational equilibrium |
torques cancel out (t=0) rotational acceleration = 0 |
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inertia |
resistance to acceleration |
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translational and rotational inertia |
rotational= moment of inertia= I= resistance to rotational accerlation mass closer to rotation axis gives smaller I mass= translational inertai |
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torque of rotational inertia |
t= Ia (rotational inertia x rotational acceleration) |
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center of mass center of gravity |
xcm (cg) = (m1x1 + m2x2 + m3x3) / (m1+m2+m3) |
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Work is positive when… |
When the angle is greater than 0 but less than 90° cosine of Theta is positive |
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Work is zero when… |
Theta equals 90° Cosine theta is zero |
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Work is negative when… |
Theta is greater than 90° but less than 180° Cosine theta is negative |
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If force is not constant and graph is given of force versus position, then the work done by that force is equal to… |
The area under the curve |
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Work done by gravity depends only on… |
The initial and final height of the object, not on the path the object follows |
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Total ME if there is friction/ outside forces |
Ei + WbyF = Ef KEi + PEi + WF = KEf + PEf |
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Inclined plane Fapp, d, and work |
Fapp >_ mgsin(theta)
d= h/ (sin(theta))
Wramp = Fapp * d = mgsin(theta) * (h/ sin theta) = mgh |
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Mechanical Advantage |
Resistance force / effort force Fr/ Feffort |
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Resistance force |
Force that would be applied if no machine were used |
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Efficiency % |
Woutput / energy input |
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Impulse |
F * dt = dp J |
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Law of conservation of momentum |
dp system = 0 Total p initial = total p final |
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Elastic collision |
Total momentum and total kinetic energy are conserved |
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Inelastic collision |
Total momentum is conserved but total Kinetic energy is not |
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Perfectly inelastic |
An inelastic collision in which the objects stick together afterwards |
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Angular momentum |
L = lmv = Iw w is angular velocity |
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Specific gravity |
Density of substance/ density of water p/ph2o |
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Shear strain |
Distance of shear/original length X/ L0 X= FL0 / AG |
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Density of ideal gas |
pgas = m / V = mP / nRT |
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Fgrav for liquids |
pVg |
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Fbuoy |
pfluid Vsub g |
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apparent weight |
Wapp = w - Fbuoy |
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Force surface tension |
2y L y is coefficient of surface tension |
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Efflux speed |
v = sqrt(2gD) |
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Poiseuille's law |
dP/L = 8nf/ pi r^4 |
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Stress |
Force/area |
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Compressive strain |
Change in length/original length dL/ L0 dL = FL0 / EA |
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Principle of superposition |
The net electric force on a charge (q) due to a collection of other charges (Q) is equal to the sum individual forces that each of the Qs exert on q |
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Energy |
Power x time |
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Terminal voltage |
If battery is supplying current then V = e - Ir
If circuit is supplying current then V = e + Ir |
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Ed's formula |
V = Ed |
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Electrical PE stored in a capacitor |
PE = (1/2) QV = (1/2) CV^2 = Q^2/2C |
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Vrms |
V / sqrt(2) |
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Energy |
Power x time |
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Terminal voltage |
If battery is supplying current then V = e - Ir
If circuit is supplying current then V = e + Ir |
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Ed's formula |
V = Ed |
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Electrical PE stored in a capacitor |
PE = (1/2) QV = (1/2) CV^2 = Q^2/2C |
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Vrms |
V / sqrt(2) |
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Irms |
I / sqrt(2) |
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Magnetic Force |
FB = q (v x B) = q vBsin(theta) |
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Do magnetic forces do work? |
No because they are always perpendicular to velocity of charge KE is constant |
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Lorentz force |
Total electromagnetic force |
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Magnetic field line on magnet emanate from? |
North Pole curling towards South Pole |
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Hooke's Law |
F = -kx |
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Elastic Potential Energy |
PE = 1/2 kx^2 |
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Restoring force |
Provided by spring Force that maintains oscillations |
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Work by spring |
-dPE elastic |
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Work by spring |
-dPE elastic |
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Work against spring |
dPE elastic |
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Amplitude |
Max displacement of block from equilibrium |
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Dynamics of oscillations |
Magnitude of restoring force is max at -A , A Magnitude of acceleration is max at -A, A PE of spring max at -A, A KE max at x=0 Speed max at x=0 |
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v max of spring |
v = A sqrt(k / m) |
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Frequency of spring |
1/(2 pi) sqrt(k / m) |
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Frequency of spring |
1/(2 pi) sqrt(k / m) |
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Period of spring |
T = 2pi sqrt(m / k) |
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Restoring force of pendulum |
Gravity Equilibrium at theta = 0 |
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Frequency of pendulum |
1/(2pi) sqrt(g / l) |
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Frequency of pendulum |
1/(2pi) sqrt(g / l) Not affected by mass |
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Period of pendulum |
2pi sqrt(l / g) Not affected by mass |
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v max of pendulum |
v = sqrt( 2 gh) |
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Conversion between degrees and radians |
180 degrees = pi radians |
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Transverse wave |
Wave propagates in direction perpendicular to direction in which medium is vibrating
Ex: wiggling one end of rope |
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Wavelength and amplitude of wave |
Wavelength is distance from crest to crest Amplitude is maximum displacement from equilibrium and does NOT depend on f, v, or lambda |
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Wave equation |
v = lambda f |
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Two big rules for waves |
1: speed of wave is determined by type of wave and characteristics of medium NOT frequency (exception is light waves: greater freq, slower speed, greater bend for refraction)
2: when a wave passes into another medium, its speed changes, but its frequency does NOT |
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Longitudinal waves |
The direction in which the particles of the conducting medium oscillate is parallel to the direction in which the wave travels |
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Speed of sound equation |
v = sqrt( B / p) B is bulk modulus (resistance to compression) and p is density |
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Speed of sound in air |
340 m/s |
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Open end of pipe corresponds to? |
Displacement Antinode (dmax) Pressure nodes (constant pressure) |
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Closed end of pipe corresponds to? |
Displacement node (no motion) Pressure antinode ( max pressure fluctuations) |
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Open pipe wavelength and frequency |
Lambda = 2L / n f = nv / 2L |
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Closed pipe wavelength and frequency |
Lambda = 4L / n f = nv / 4 L n is odd number |
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Max and min amplitude sounds |
Max is loud Min is soft |
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Beats |
Resulting equally spaced moments of constructive interference ( the loud moments) |
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Beat frequency |
Fbeat = ( f1 - f2 ) |
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Constructive interference |
Crest meets crest amplitudes add |
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Intensity and it's relation to r and A |
The energy a sound wave transmits per second ( the power) per unit area
I inversely proportional to r^2 I proportional to A^2 |
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Threshold of hearing |
Lowest intensity human can hear 10^-12 I0 |
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Intensity level |
B = 10 log I / I0 Usually multiply by 10 to get decibels dB |
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Important relationship of intensity level equation |
Every time we multiply I by 10 we add 10 to B Every time we divide I by 10 we subtract 10 from B |
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Doppler effect theory |
Approaching - higher detected frequency Receding - lower detected frequency Detector moves away/near relative speed changes with constant wavelength Source moves wavelength changes with constant speed |
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Doppler effect equation |
fD = fs (v +/- vD ) / ( v -/+ vs)
v is speed of wave
Top sign is toward |
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Electromagnetic waves are? |
Transverse waves Oscillate with same frequency at which electric charge does In phase Perpendicular to each other Direction of propagation (polarization) |
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Electromagnetic waves speed equation |
c = lambda f |
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Increasing frequency and energy of EM waves Decreasing wavelength |
Radio, micro, infrared, visible (ROYGBIV), UV, X-rays, gamma rays |
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Photon energy |
E = hf = h (c / lambda) |
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Destructive interference |
Crest coincides with trough Amplitudes subtract |
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Plancks constant |
h = 6.6 x 10^-34 |
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Law of reflection |
Angle of reflection is equal to angle of incidence Angle with normal |
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Index of refraction |
n = c / v
v is speed of light in medium n = 1 for air and vacuum n is never less than 1 and the greater the value the slower light travels in the medium |
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Law of refraction ( snells law) |
n1 sin theta1 = n2 sin theta2
If n2 > n1 theta 2 < theta 1, ray will bend toward normal If n2 < n1 theta 2 > theta 1, ray will bend away from normal |
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Critical angle for total internal reflection |
Sin thetacrit = n2/n1 |
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Turning unpolarized light into polarized |
Use of polarizing filter |
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Concave mirror focal length |
f = 1/2 r Object farther than focal point: image will appear at focal point Real in front of mirror inverted Halfway between C and mirror
Object inside focal point: image forms behind mirror Virtual upright |
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Convex mirror focal point |
Imaginary/ virtual behind mirror so it is upright |
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Mirror lens equation |
(1/o) + (1/i) = (1/f)
o is objects distance from mirror (always positive) f is focal length i is the images distanxe from mirror ( positive means in front and real; negative means behind and virtual) |
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Magnification equation |
m = - i / o Multiplying the height of object by m gives the height of image Positive- upright Negative- inverted Real images are inverted and virtual are upright |
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Path differences for waves |
= n lambda waves in phase = (n + 1/2) lambda waves out of phase |
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Converging lens (convex) |
Thicker in middle Refract light rays that are parallel to axis toward focal point on other side of lens F is positive Real and virtual |
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Diverging lens (concave) |
Are thinner in the middle and refract light rays that are parallel to the axis away from the imaginary focal point that's in front of the lens
F is negative Only virtual in front of lens |
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Lens power |
P = 1/f P = P1 + P2 |
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Myopia |
Nearsightedness Diverging lens correction |
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Hyperopia |
Farsightedness Converging lens correction |
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Accommodation |
Ability to focus on near by objects through the action of the ciliary muscles which essentially squeeze lens of the eye increasing its curvature and decreasing it's focal length |
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First harmonic (fundamental) |
Lambda = 2L / 1 |
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Second harmonic |
2L / 2 |
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Third harmonic |
2L / 3 |
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Standing waves for wavelengths for two fixed ends |
2L / n |
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Standing wave frequencies for two fixed ends |
(n / 2L) (v) |
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Using fundamental frequency to find all other harmonic frequencies |
fn = nf1 |
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Two big rules for waves |
1: speed of wave is determined by type of wave and characteristics of medium NOT frequency (exception is light waves: greater freq, slower speed, greater bend for refraction)
2: when a wave passes into another medium, its speed changes, but its frequency does NOT |
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Longitudinal waves |
The direction in which the particles of the conducting medium oscillate is parallel to the direction in which the wave travels |
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Speed of sound equation |
v = sqrt( B / p) B is bulk modulus (resistance to compression) and p is density |
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Speed of sound in air |
340 m/s |
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Open end of pipe corresponds to? |
Displacement Antinode (dmax) Pressure nodes (constant pressure) |
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Closed end of pipe corresponds to? |
Displacement node (no motion) Pressure antinode ( max pressure fluctuations) |
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Open pipe wavelength and frequency |
Lambda = 2L / n f = nv / 2L |
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Closed pipe wavelength and frequency |
Lambda = 4L / n f = nv / 4 L n is odd number |
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Max and min amplitude sounds |
Max is loud Min is soft |
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Beats |
Resulting equally spaced moments of constructive interference ( the loud moments) |
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Beat frequency |
Fbeat = ( f1 - f2 ) |
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Constructive interference |
Crest meets crest amplitudes add |
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Intensity and it's relation to r and A |
The energy a sound wave transmits per second ( the power) per unit area
I inversely proportional to r^2 I proportional to A^2 |
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Threshold of hearing |
Lowest intensity human can hear 10^-12 I0 |
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Intensity level |
B = 10 log I / I0 Usually multiply by 10 to get decibels dB |
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Important relationship of intensity level equation |
Every time we multiply I by 10 we add 10 to B Every time we divide I by 10 we subtract 10 from B |
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Doppler effect theory |
Approaching - higher detected frequency Receding - lower detected frequency Detector moves away/near relative speed changes with constant wavelength Source moves wavelength changes with constant speed |
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Doppler effect equation |
fD = fs (v +/- vD ) / ( v -/+ vs)
v is speed of wave
Top sign is toward |
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Electromagnetic waves are? |
Transverse waves Oscillate with same frequency at which electric charge does In phase Perpendicular to each other Direction of propagation (polarization) |
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Electromagnetic waves speed equation |
c = lambda f |
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Increasing frequency and energy of EM waves Decreasing wavelength |
Radio, micro, infrared, visible (ROYGBIV), UV, X-rays, gamma rays |
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Photon energy |
E = hf = h (c / lambda) |
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Destructive interference |
Crest coincides with trough Amplitudes subtract |
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Plancks constant |
h = 6.6 x 10^-34 |
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Law of reflection |
Angle of reflection is equal to angle of incidence Angle with normal |
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Index of refraction |
n = c / v
v is speed of light in medium n = 1 for air and vacuum n is never less than 1 and the greater the value the slower light travels in the medium |
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Law of refraction ( snells law) |
n1 sin theta1 = n2 sin theta2
If n2 > n1 theta 2 < theta 1, ray will bend toward normal If n2 < n1 theta 2 > theta 1, ray will bend away from normal |
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Critical angle for total internal reflection |
Sin thetacrit = n2/n1 |
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Turning unpolarized light into polarized |
Use of polarizing filter |
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|
Concave mirror focal length |
f = 1/2 r Object farther than focal point: image will appear at focal point Real in front of mirror inverted Halfway between C and mirror
Object inside focal point: image forms behind mirror Virtual upright |
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Convex mirror focal point |
Imaginary/ virtual behind mirror so it is upright |
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|
Mirror lens equation |
(1/o) + (1/i) = (1/f)
o is objects distance from mirror (always positive) f is focal length i is the images distanxe from mirror ( positive means in front and real; negative means behind and virtual) |
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Magnification equation |
m = - i / o Multiplying the height of object by m gives the height of image Positive- upright Negative- inverted Real images are inverted and virtual are upright |
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Path differences for waves |
= n lambda waves in phase = (n + 1/2) lambda waves out of phase |
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Converging lens (convex) |
Thicker in middle Refract light rays that are parallel to axis toward focal point on other side of lens F is positive Real and virtual |
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Diverging lens (concave) |
Are thinner in the middle and refract light rays that are parallel to the axis away from the imaginary focal point that's in front of the lens
F is negative Only virtual in front of lens |
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Lens power |
P = 1/f P = P1 + P2 |
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Myopia |
Nearsightedness Diverging lens correction |
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Hyperopia |
Farsightedness Converging lens correction |
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Accommodation |
Ability to focus on near by objects through the action of the ciliary muscles which essentially squeeze lens of the eye increasing its curvature and decreasing it's focal length |
|
|
First harmonic (fundamental) |
Lambda = 2L / 1 |
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Second harmonic |
2L / 2 |
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Third harmonic |
2L / 3 |
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Standing waves for wavelengths for two fixed ends |
2L / n |
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Standing wave frequencies for two fixed ends |
(n / 2L) (v) |
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Using fundamental frequency to find all other harmonic frequencies |
fn = nf1 |
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Energy of photon |
E photon = hf = hc/ lambda h is plancks constant = 6.63 x 10^-34 |
