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:-
- 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 ?