A Doppler Effect problem with a moving medium

Question

I tried solving the following question and started having multiple doubts:

Two cars A and B are moving towards each other with some speed $25$ m/s. Wind is blowing with speed $5$ m/s in the direction of car A. The car A blows horn of frequency $300$ Hz and the sound is reflected from car B. What is the wavelength of the reflected sound received by the driver of car A? Assume that the velocity of sound in air is $330$ m/s.

My doubts are:

1) In Doppler effect problems, we talk about apparent frequency and not the actual frequency. My understanding is that the rate at which I will see crests (or troughs) at a point is affected by the speed with which the wave is arriving at the point and thus the frequency looks different.

So would it be right to say that when the wave is reflected from B, we can think of it as a source kept on the car B?

2) Due to the speed of the wind, can we substitute the relative velocity of the source and the receiver in the formula? I am assuming that the usual formula for Doppler effect is derived assuming that the medium is at rest.

3) Finally, does the wavelength of sound change if the medium is moving? In particular, if the wind is blowing at the speed of sound in the same direction as sound, what would be it's wavelength?

I would also appreciate an answer for this problem, rather than a detailed solution. I would love insightful hints as well.

Thank you for your help :)

Answer 1

Here's a similar question which will be helpful to resolve your apparent perception of Doppler effect. Because, Doppler effect is real.

So would it be right to say that when the wave is reflected from B, we can think of it as a source kept on the car B?

No. Because the frequency has already been altered (probably increased) by the moving car and the wind (which can be found using classical velocity addition) and finally, the high frequency sound has been returned to B, which reflects it back - which again gets altered by velocity of B and wind flowing in opposite direction.

Due to the speed of the wind, can we substitute the relative velocity of the source and the receiver in the formula?

You should use the velocity addition formula. Don't forget to account for wind too...

Does the wavelength of sound change if the medium is moving? In particular, if the wind is blowing at the speed of sound in the same direction as sound, what would be it's wavelength?

The speed of sound is a constant at a particular medium. So, if the frequency of sound changes, the wavelength should also change in order for $c$ to be constant. If the wind is blowing the opposite direction to the source of sound at $c$ (no relativistics...), the wavelength is $0$. Because, always keep in mind the sound is pushing & pushing & pushing of the molecules. If there's an opposition pushing it with the same velocity, then its whole energy would be spent trying to oppose wind and finally FAIL...