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44 Cards in this Set
- Front
- Back
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Principle of superposition |
states that when 2 or more waves meet at a point, the resultant displacement at that point is equal to vector sum of the displacement of each waves at that point |
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Stationary wave |
a wave that has a waveform that does not advance. Characterized by presence of node & antinode It is formed when 2 waves of equal frequency & amplitude travelling along the same line with the same speed buy in opposite direction superposed. |
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Characteristics of stationary wave nodes: |
Nodes are points along the stationary wave at which displacement is always zero (zero amplitude) |
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Characteristics of stationary wave antinodes: |
Antinodes are points along the stationary wave at which displacement is always max (max amplitude) |
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Phrases in stationary wave |
All points within the same loop are in phrase with one another Antiphrase with all the points in the adjacent loop |
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Energy transfer |
Energy is not transferred but stored in a stationary wave. Energy is maximum for particles at the antinode, min at nodes |
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Harmonics |
Modes of vibration present in any vibrating system. |
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Fundamental frequency |
lowest frequency obtainable from the possible harmonics. It is known as the first harmonic |
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Overtones |
are the higher frequency that occur simultaneously with the fundamental frequency. Constitute harmonics higher then the first. |
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Conditions of a well defined stationary wave |
Component waves must travel with same speed but in opposite direction. Must overlap Must have roughly the same amplitude Must have same frequency |
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wavelength & frequency of Nth harmonics |
(N-1)th overtone wavelength : L=Nλ/2 λ=2L/N frequency: fn=v/λn= Nv/2L= Nf1 |
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stationary sound wave in a closed air column |
First point of resonance, λ/4 = L1 +e 2nd point of resonance, 3λ/4=L2+e subtracting, 2λ/4= L2-L1 speed of sound= v=λf= 2f(L2-L1) |
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relationship between displacement and pressure changes of stationary sound waves |
Unbroken line in disp-dist graph corresponds to the unbroken line in pressure-dist. graph At displacement nodes: air particles stationary,pressure max---pressure antinodes At displacement antinodes pressure change 0---pressure nodes |
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Modes of vibration for stationary longitudinal waves |
General expression for the frequency fn of the nth mode of vibration of the air in closed tube nth harmonic / (n-1)th overtone is fn=(2n-1)v/4L wavelength general expression λ =4L/(2n-1) closed end always node (disp), antinode (pressure) open end always antinode (disp), node (pressure) |
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Modes of vibration for stationary longitudinal waves in an open pipe |
General expression for the frequency fn of the nth mode of vibration of the air in closed tube nth harmonic / (n-1)th overtone is fn=nv/2L = nf wavelength general expression λ=2L/n |
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Huygen's principle |
every point on a wave front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of the wave. The new wave front is the tangential surface to all of these secondary wavelets |
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interference |
Process in which 2 more waves of the same frequency superpose to either reinforce or cancel each other. To produce a new wave pattern with a change in amplitude/ intensity |
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constructive interference
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When 2 or more waves meet at a point such that the resultant displacement is greater than the largest individual displacement Fully constructive interference occurs when the 2 waves meet in phase |
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destructive interference |
When 2 or more waves meet at a point such that the resultant displacement is less than the largest individual displacement. Fully destructive interference occurs when 2 waves have the same amplitude and meet anti-phase |
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Coherent waves |
2 waves are coherent if there is a constant phrase difference between them frequency of the waves are the same |
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Conditions for an interference pattern formed |
2 waves must overlap 2 waves must of the same kind 2 waves must be polarised in the same plane or both unpolarised ( for em waves) |
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Why amplitude of each wave must be approx. same for interference pattern to be observable
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So that there is total cancellation of wave amplitude at DI At CI, addition of wave amplitude gives high intensity so, that there is good contrast |
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Why source of each wave must be coherent for interference pattern to be observable
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This is so that the pattern of maxima and minima does not change with time |
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For interference pattern of transverse waves to be observable (polarization) |
2 waves must be polarised in the same plane or both unpolarised
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In phase source, CI occurs when |
Constructive (maxima occurs When the path difference equal to an integer number multiple of a wavelength ( λ,2λ,3λ...) Δx=xλ ΔØ=nλ(phrase difference) |
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in phase sources, DI occurs when
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Destructive
When the path difference equal to an odd integer multiples of half a wavelength (λ/2, 3λ/2, 5λ/2) Δx=(n+1/2)λ ΔØ=(2n+1)pi |
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antiphrase sources , CI |
CI When the path difference equal to an odd integer multiples of half a wavelength (λ/2, 3λ/2, 5λ/2) Δx=(n+1/2)λ ΔØ=(2n+1)pi |
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antiphrase sources, DI
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DI
When the path difference equal to an integer number multiple of a wavelength( λ,2λ,3λ...) Δx=xλ ΔØ=nλ(phrase difference) |
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diffraction |
spreading out of waves after passing an aperture or when it encounters an obstacle |
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Condition for observable diffraction patter |
size of aperture/slit must be close to the wavelength of the incident wave
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Single slit diffraction of light waves Central maximum fringe |
The widest & brightest & is flanked by subsidiary maxima which are less intense |
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Location of minima for single slit diffraction |
For n minima sinØdark = +/- nλ/a where a is the slit width where Ø is the angular spread of the incoming wave on the screen. |
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Width of the central maxima depends on |
Wavelength of light (increasing λ, increasing width) width of slit (decreasing a, increasing width) slit-screen distance,L |
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Compare intensity of first and second maxima with central maxium |
First is 5% of central Second is 2% of central Third is 1% of central |
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Rayleigh's criterion |
Two images formed by a slit are just a distinguishable if the central maximum of the diffraction pattern for one object must fall on the first min. of the diffraction pattern of the other. |
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Minimum angle of resolution for a slit a width a is |
Ømin= λ /a |
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To be able to distinguish 2 images |
s/r greater then λ/a s: separation of the 2 objects r: distance between object and aperture |
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resolution can be improved by |
Using light of shorter wavelength larger aperture with (increase a) |
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Scientific implication of Young's double slit experiment |
It shows that light is a wave and can undergo diffraction and forms interference wavelength of visible light is in the order of 10^-7 |
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For double slit interference, the relation between the wavelength or the monochromatic light and the fringe seperation is given by |
λ=(slit separation x fringe seperation)/ perpendicular distance between slits & screen =ax/D |
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assumption in double slit interference formula |
D is much larger then a perpendicular distance between slits is much larger then slit seperation |
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diffraction grating bright fringes are separated at angle Ø is given by |
dsinØ=nλ n is the order of the bright fringes from the centre line λ is the wavelength of the chromatic light d is the seperation of the slits |
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seperation of the slits |
slit seperation,d 1 metre/number of line per meter
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Energy redistribution for 2 source interference |
CI Ar=A+A=2A Ir=4I (since I=kA^2) DI Ar=A-A=0 Ir= 0 |
