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PHY 102: Waves & Quanta Topic 5 Sound John Cockburn (j.cockburn@... Room E15) PowerPoint Presentation
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PHY 102: Waves & Quanta Topic 5 Sound John Cockburn (j.cockburn@... Room E15). Sound Waves Speed of sound in fluids in fluids, gases and solids Doppler Effect Beats. Sound waves. Unlike waves on a string (transverse waves), sound waves are longitudinal waves

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slide1

PHY 102: Waves & Quanta

Topic 5

Sound

John Cockburn (j.cockburn@... Room E15)

slide2

Sound Waves

  • Speed of sound in fluids in fluids, gases and solids
  • Doppler Effect
  • Beats
slide3

Sound waves

  • Unlike waves on a string (transverse waves), sound waves are longitudinal waves
  • Particles undergo SHM about equilibrium positions PARALLEL to direction of wave propagation
  • Compression/rarefaction of the medium through which the sound wave travels………………………………………………
  • Wave travelling from left to right/right to left still described by:

But this time, y is in same direction as x……

slide4

Sound waves

(Ear, for example

is sensitive to pressure, not dislacement

Fluctuations)

slide5

Speed of sound

In a fluid:

Bulk modulus

density

In a solid rod:

Young’s modulus

slide7

The Doppler Effect

  • If we stand still near a source of sound, and the source is also not moving we hear sound of a certain frequency f0
  • If either, or both, the listener and the source are moving relative to one another, then a different frequency fL is heard by the listener.
  • In general, if the listener and the source are moving towards each other, fL > f0, ie a higher pitch is heard.
  • If the listener and the source are moving away from each other, fL<f0, ie a lower pitch is heard.
  • This is known as the Doppler Effect
  • Ambulance sirens, car horns, etc. etc.
slide8

Explanation of the Doppler Effect

Listener moving towards stationary source with velocity vL

slide9

Explanation of the Doppler Effect

Effective velocity of sound heard by listener = vL+v:

Moving listener, stationary source

slide10

Moving Source

It takes a time T for one complete cycle of the wave to be emitted.

(T = 1/f0)

During this time, the wavefront has moved a distance vT, and the source has moved a distance vsT

The wavelength is:

In front of source

Behind source

slide11

Moving listener approaching moving source

(Stationary source, earlier slide)

(Modified λ, due to moving source)

slide12

And now the good news……………………

Works for ALL relative motions of source and listener in acoustic Doppler shift calculations, PROVIDED you DEFINE the positive direction as the listener to source direction, and set the signs of vL and vs accordingly……………………………………………………………………………………

slide13

Example calculations

Two train whistles A and B each have a frequency of 392 Hz. A is stationary, while B is moving to the right, away from A, at a speed of 35ms-1. A listener is between the 2 trains and is also moving to the right, with a speed of 15ms-1. What frequencies does the listener hear from whistles A and B?

(speed of sound in air = 340ms-1)

slide14

Whistle A

Positive direction

slide15

Whistle B

Positive direction

slide16

A police car (whose driver has clearly been watching too much Starsky and Hutch), with a 300Hz siren is approaching a warehouse at 30ms-1 with the intention of crashing through the door. What frequency does the driver hear reflected from the warehouse?

(speed of sound in air = 340ms-1)

Two part question………………………..

slide17

In the first part, treat the warehouse door as the “listener”…..

Sound at this frequency is reflected back towards the police car. This becomes the “new” f0 for the 2nd part of the question…………………..

slide19

Beats

These occur from the superposition of 2 waves of close, but different frequency: