I am so confused about the following relativity question. Please help me with the 3 conditions!?

Question

1-Is the following statement for two people, standing still in an air current, hearing the sound correct or not. Please help.

In a (moving) current of air, two people standing still at the two opposite sides of a sound source by the same distance from the sound source, will perceive the speed of sound differently (one higher and the other one lower than sound speed in still air) but this difference in perceived speed has no time effect, i.e. they both receive the sound at the same time despite their different perceived sound speed (is this correct?). However, the perceived difference in speed shows itself as difference in pitch of the sound heard by these two people. The person, who perceives the speed of sound higher than its normal speed in still air, will hear higher pitch and the other one, who perceives the speed of sound lower than its normal speed in still air, will hear lower pitch. And this is where the difference is perceived speed of sound for these two people shows itself.

2-What happense if these two people are in a moving OPEN train with speed 'x' m/s; one in front wagon & the other in the back wagon with sound source in the middle of train. Who hears the sound first?

3-If the train is close (air cannot flow in or out of it), who hears the sound first?

Answer 1

The first statement is wrong and this is, indeed, the profound difference between sound and light as explained by the theory of Relativity.

With sound, one person will hear it earlier than the second.

With light, both persons will see it at the same moment.

For both sound and light, there will be a pitch change. For light, it is the so-called red-shift (galaxies moving away from us) or blue-shift (galaxies moving toward us, like Andromeda).

It was first thought that light was moving into something called the aether. But it couldn't be measured and therefore came the fundamental principle of Relativity: The speed of light is constant and everything is observed from the observer's own frame of space, time and inertia.

The person being downwind will hear the sound sooner and in a lower pitch.

If they are both in an open moving vehicle, the reception time delay will be the same because the relative difference of speed will also be the same but the pitch will be higher and lower because the absolute speed will be much higher.

If the vehicle is enclosed, the there won't be a difference from a motionless vehicle.

In all three cases, the person downwind will hear the sound first.

Answer 2

EDITED --- my first response was incorrect

1 is false. The motion of the air will cause the ground-relative speed of the sound to be lower in the upwind direction, compressing the peaks of the wave together, but the observer will get the peaks more slowly than normal due to the same motion of the air, so the frequency will be unchanged. The downwind observer will hear the sound first because the speed of sound is higher in that direction relative to the ground, but the frequency will also be unchanged for the same reason as the upwind observer.

2) This situation is identical as problem 1. The motion of the ground under the train is irrelevant in the frame of the sound source, observers, and air. To an observer on the train, the air is moving by just as it was in the wind tunnel / air current of problem 1. The sound is affected in the same ways as problem 1, so the front observer hears the sound later than the rear observer, both with no doppler shift.

3) both observers hear the sound simultaneously since the air is stationary in their frame of reference, as is the sound source and are both observers. No doppler shift here either.

Answer 3

1.  I think the downwind person would actually hear the sound earlier than the upwind person.  Sound propagates through air of a given density and temperature at a constant rate.  So, if the air is moving toward you the sound in the air will reach you more quickly, and will have a higher pitch.

2.  In a moving, open train the situation is somewhat different, but I think the effect is the same.  The sound source emits its sound at point 'A', which, in effect, moves at X m/s away from the source.  So, the person at the rear of the train moves toward point 'A' (at X m/s), while the air and sound moves toward the back of the train at 335 m/s + X m/s.  Hence the rearward person will hear the sound more quickly, and at a higher pitch.

3.  If there is no air motion in the train, the sound gets to each person at the same point in time (the air is not moving relative to the source of sound or to the two people in question.  The fact that the train is moving does not affect the speed of sound within it.  If this were not so, then those who flew in the Concorde SST at twice the speed of sound would either hear very high pitched voices when listening to their neighbor in front of them or nothing at all listening to those behind them.  Also, Earth (and it's atmosphere) rotates at about 1600 km/hour (at the equator) and there is no effect on sound properties facing either eastward or westward.