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What frequency sound would be observed by observer at rest is source is moving away from him at speed of sound? And Why so?

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This can be derived from the doppler frequency shift equation with reference to a stationary observer.

f = f'(v/v+v')

where:

  • v is the speed of sound in a medium
  • v' is the speed of the source
  • f' is the source frequency
  • f is the apparent frequency

if the speed of the source (v') equals the speed of sound (v) then the equation folds down to:

f = f'(v/2v) = f'/2

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Half the original frequency. If you listen to the sound that is happening 1 second later, it arrives with an additional delay of 1 second due to the sound propagation. So the phase moves forward at half the original speed.

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