Question

A girl is sitting near the open window of a train that is moving at a velocity of 22.00 m/s to the east. The girl's uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at frequency 770.0 Hz. The air is still. (Use 343 m/s for the speed of sound in air for all parts of this question.) (a) What frequency does the uncle hear? Hz (b) What frequency does the girl hear? Hz (c) A wind begins to blow from the east at 22.00 m/s. What frequency does the uncle now hear? Hz (d) What frequency does the girl now hear? Hz

Answer 1

Frequency heard = f
Speed of sound through the medium = c
Speed of the receiver through the medium =Vr
Spreed of the source through the medium = Vs
Initial frequency = fi

f = [(c + Vr) / (c + Vs)] * fi

a) fi = 770 Hz
c = 343 m/s
Vr = 0 m/s (the uncle does not move relative to the air)
Vs = 22 m/s ( the whistle moves 10 m/s relative to the air, and it is positive because the direction is away from the receiver.)

f = [(343 m/s + 0 m/s) / (343 m/s + 22 m/s)] * 770 Hz

f= 723.58 Hz

b) In this case Vs is still 22 m/s, but so the speed of the girl relative to the air is also 10 m/s in the same direction

f = [(343 m/s + 22 m/s) / (343 m/s + 22 m/s)] * 770 Hz

f = 770 Hz.

c) And now for the wind. Yes,when they say that the wind if FROM the east, then it is blowing TO the west, or against the motion of the train. It is an old tradition thing from long before weathermen to describe a wind based on the direction that it comes from.

OK, here Vs is 22 m/s away from the receiver because of the motion of the train relative to the ground and, yes, another 22 m/s because of the wind is blowing 10 m/s relative to the ground. SO the speed of the whistle relative to the AIR is 44 m/s and is positive. Now what about the uncle? The uncle is moving 22 m/s towards the train, relative to the air. (He is not actually moving, the air is passing by him at 22 m/s. They say "towards the train" just to give you the direction, for the plus or minus in your equation. The uncle' position on the train platform does not change, but Vr is relative to the WIND and in the DIRECTION of the train).

The whole relativity can get confusing, but think of yourself traveling along with the wind. From your point of view it looks as though the uncle is moving east, instead of you moving west. Did I say that badly?

f = [(343 m/s + 22 m/s) / (343 m/s + 44 m/s)] * 770 hz

f = 726.22 Hz

d) This is like c) Vs = 44 m/s, but Vr also = 44 m/s relative to the wind, so the cancel each other out again.

f = 770 Hz