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 :)