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A source emits sound of frequency $f$ and speed of sound in the medium(here, air) is $330 m/s$. If the source acquires a velocity ‘v’ w.r.t. the medium, what is the wavelength of sound emitted from the source in the direction of its motion?

My approach to this question first brings a question:-

  1. Will the speed of the emitted sound wave be $330 m/s$ or it will be a different value? Why and why not?

I’ve found that it will be $330 m/s$, or the speed of the sound wave w.r.t the medium irrespective of the relative motion of the source with the medium.

Then I have the equation:- $ v=f* \lambda $

Let’s assume at $t=0$ first wavefront(crest) was created in a medium. At time $t=1/f$, next wavefront will be created.

The distance between these two wavefronts is:-

$ 330/f - v/f$

As in $1/f$ time, the source will have covered $v/f$ distance too

which is the wavelength of the sound wave. I interpret from the above derivation that speed of sound indeed changed and frequency remained unchanged, though this could be wrong on my part as I am applying Doppler effect here. What is wrong with my interpretion ?

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You are talking about a Doppler effect with the source moving toward the observer. The speed of the wave is determined by the medium and does not change. If the observer is stationary, he will see a shorter wavelength and hear a higher frequency. The classic example is standing on a corner when a car goes by with its horn blowing. There will be a noticeable drop in the frequency (pitch) of the sound from the horn as it goes from approaching to receding.

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  • $\begingroup$ What happens in the case of the medium in motion? If wind has some velocity, I believe speed of sound w.r.t air when there is wind is equal to speed of sound w.r.t still air. $\endgroup$ – Ashish Raj Shukla Jul 17 at 18:07
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    $\begingroup$ Measure all speeds relative to the medium (air). $\endgroup$ – R.W. Bird Jul 17 at 18:20

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