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Doppler Effect for Sound Waves (CIE A Level Physics)

Revision Note

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Katie M

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Doppler shift of sound

  • The whistle of a train or the siren of an ambulance appears to decrease in frequency (sounds lower in pitch) as it moves further away from you
  • This frequency change due to the relative motion between a source of sound or light and an observer is known as the doppler effect (or doppler shift)
  • When the observer (e.g. yourself) and the source of sound (e.g. ambulance siren) are both stationary, the waves are at the same frequency for both the observer and the source

Waves emitted from a stationary source

Doppler shift diagram 1, downloadable AS & A Level Physics revision notes

According to the observer stationary relative to the source, the frequency is equal to that measured by the source

 

  • When the source starts to move towards the observer, the wavelength of the waves is shortened
    • The sound therefore appears at a higher frequency to the observer

Waves emitted by a moving source

8-2-2-4-double-slit-equation

The source and observer disagree on their measurements of the frequency of the wave

 

  • Notice how the waves are closer together between the source and the observer compared to point P and the source
  •  If the observer was at point P instead, they would hear the sound at a lower frequency due to the wavelength of the waves broadening

 

  • The frequency is increased when the source is moving towards the observer
  • The frequency is decreased when the source is moving away from the observer

Worked example

A cyclist rides past a stationary observer ringing their bell as they ride away.

Which of the following accurately describes the Doppler shift caused by the sound of the bell as the cyclist moves away from the observer?

  Wavelength Frequency Pitch
A Shorter Higher Higher
B Longer Lower Higher
C Shorter Higher Lower
D Longer Lower Lower

 

Answer:  D

  • As the cyclist rides away from the observer, the wavelength increases or becomes longer
    • This rules out options A and C
  • A longer wavelength means a lower frequency (from the wave equation v space equals space f lambda)
  • A lower frequency corresponds to a sound of lower pitch
    • Therefore, the correct answer is D

Calculating Doppler shift

  • When a source of sound waves moves relative to a stationary observer, the observed frequency can be calculated using the equation below:

f subscript o space equals space f subscript s open parentheses fraction numerator v over denominator v space plus-or-minus space v subscript s end fraction close parentheses

  • Where
    • fo is the observed frequency in Hz
    • fs is the source frequency in Hz
    • is wave velocity in m s−1
    • vs is the velocity of the source relative to the observer, again in m s−1
  • The wave velocity for sound waves is 340 ms-1
  • The ± depends on whether the source is moving towards or away from the observer
    • If the source is moving towards, the denominator is v - vs
    • If the source is moving away, the denominator is v + vs

Worked example

A police car siren emits a sound wave with a frequency of 450 Hz. The car is travelling away from an observer at speed of 45 m s-1. The speed of sound is 340 m s-1.

Which of the following is the frequency the observer hears?

A. 519 Hz               B. 483 Hz               C. 397 Hz               D. 358 Hz

Answer: C

Step 1: Choose the correct version of the Doppler shift equation:

  • The source is moving away from the observer so choose the plus symbol

f subscript o space equals space f subscript s open parentheses fraction numerator v over denominator v space plus space v subscript s end fraction close parentheses

Step 2: Substitute the given values:

  • The observer's recording of frequency is

f subscript o space equals 450 space cross times space open parentheses fraction numerator 340 over denominator 340 space plus space 45 end fraction close parentheses space equals space 397 space Hz

Examiner Tip

Be careful as to which frequency and velocity you use in the equation. The ‘source’ is always the object which is moving and the ‘observer’ is always stationary.

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.