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Physics Foundations > Travelling Waves, Standing Waves and Normal Modes > Flashcards

Travelling Waves, Standing Waves and Normal Modes Flashcards

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1
Q

How do you write the superposition of displacement of 2 waves?

A

u(x, t) = u1(x, t) + u2(x, t)

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2
Q

How is a reflected wave different to the incident wave on a hard wall?

A

incident wave: f(x-vt)
reflected wave: -f(-x-vt)
Wave inverted and travels in opposite direction.

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3
Q

What happens to a reflected wave if the boundary is a free end rather than a hard wall?

A

Incident wave: f(x-vt)
Reflected wave: f(-x-vt)
Wave travels in opposite direction. Amplitude of wave at boundary is 2x displacement.

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4
Q

What should you consider for a general case of wave reflection?

A

A plane wave propagating on a string with an amplitude of 1.

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5
Q

What will the amplitude be of the transmitted/reflected waves of this A=1 waves?

A

Transmitted A = t

Reflected A = r

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6
Q

What is the equation for a plane wave with an amlitude of 1 in complex form?

A

y(x, t) = e^(i*(kx-ωt))

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7
Q

What is the displacement at the boundary condition x=0?

A

ytot (left) = ytot (right)

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8
Q

What is the force at boundary conditions x=0?

A

TL dyL/dx = TR dyR/dx

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9
Q

What is the equation for r, the amplitude of the reflected wave at boundary condition x=0?

A

r = (ZL-ZR)/(ZL+ZR)

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10
Q

What is the equation for t, the amplitude of the transmitted wave at the boundary condition x=0?

A

t = (2ZL)/(ZL+ZR)

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11
Q

How can you use the equations for transmitted and reflected amplitudes to check limiting cases?

A

For hard wall, ZR&raquo_space; ZL

FOr free end, ZR &laquo_space;ZL

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12
Q

What is the equation for displacement of standing waves?

A

utot(x, t) = utot(x) * utot(t)

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13
Q

How many wavelengths can a standing wave between two rigid boundaries have?

A

L = n*λ/2

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14
Q

What is an antinode?

A

Parts of maximum amplitude on a standing wave.

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15
Q

What is the equation for angular frequency of a standing wave?

A

ω = npiv/L = kv

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16
Q

How does an organ pipe work?

A

Has two open ends of a tube, and there are standing waves inside with pi phase change from normal standing waves, so fundamental has 1 node rather than 1 antinode etc.

17
Q

How does a clarinet work?

A

One open end and one closed end in a tube. Closed end is a node in displacement, and openend is antinode indisplacement. Only odd nodes are allowed due to this.

18
Q

What is the condition for constructive interference in the general case of a cavity?

A

e^(ikL)re^(ikL)r = 1 = e^(i2npi)

19
Q

What are beats?

A

When 2 waves of same amplitude and similar frequencies travel in the same direction.

20
Q

How can you find the equation for beat frequency?

A

Similar frequencies, so k1 = k-Δk and k2 = k+Δk, and ω1 = ω-Δω and ω2 = ω+Δω. Substitute these into the equation anf use superposition.

21
Q

What is the equation including beat frequency?

A

utot = 2Acos(kx-ωt)cos(Δkx - Δωt). Second term is the beat frequency.

22
Q

What is the velocity of the beat wave?

A

v = Δω/Δk

23
Q

What determines if waves are dispersive or non-dispersive?

A

Dispersive - velocity changes with frequency or wavelength.

Non-dispersive - velocity does not change with frequency or wavelength.

24
Q

What is the idea of group velocity?

A

Wave packets travel at a certain velocity, but the individual waves within travel at their phase velocity.

25
Q

What is the doppler effect?

A

When the apparent frequency of a wave changes when the source or observer are moving.

26
Q

What is the equation for the wave in the frame of the medium?

A

f(x, t) = Ae^(i(kx+ωt)) = Ae^(i((ω/v)x + ωt))

27
Q

How can you convert the equation for the wave in the frame of the medium to the fram of the source and receiver?

A

Using Galileon transformations. x = xs + us t, where s denotes the source.Can change to r for receiver.

28
Q

What is the equation for frequency in the source and receiver frames?

A 
ωs = ω(1+us/v)
ωr = ω(1+ur/v)
29
Q

What are the 2 limiting cases in the Doppler effect?

A
  1. Stationary receiver, moving source - set ωr = 1

2. Stationary source, moving receiver - set ωs = 1

30
Q

What is the equation for the relativistic doppler effect?

A

ωr/ωs = sqrt((1-u/c)/(1+uc)), where u is the speed of the source in the frame of the observer.

Physics Foundations (10 decks)

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