# Characteristics of sound waves in a medium when it’s source is in motion

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 ?