A girl Is sitting near the open window of a train that Is moving at a velocity o

Question

A girl Is sitting near the open window of a train that Is moving at a velocity of 24.00 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 960.0 Hz. The air is still. (Use 343.0 m/s for the speed of sound in air for all parts of this question. Give your answers to at least four significant figures.) What frequency does the uncle hear? What frequency does the girl hear? A wind begins to blow from the east at 24.00 m/s. What frequency does the uncle now hear? What frequency does the girl now hear?

Explanation / Answer

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 =960 Hz

c = 343 m/s
Vr = 0 m/s (the uncle does not move relative to the air)
Vs = 24 m/s ( the whistle moves 24 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 + 24 m/s)] * 960 Hz

f=897.22 Hz

b)

In this case Vs is still 24 m/s, but so the speed of the girl relative to the air is also 24 m/s in the same direction

f = [(343 m/s + 24 m/s) / (343 m/s + 24 m/s)] * 960 Hz

f =960 Hz.
f = [(343 m/s +24 m/s) / (343 m/s +48 m/s)] *960 hz

f = 901.07 Hz

d)

This is like c) Vs = 48 m/s, but Vr also = 48 m/s relative to the wind, so the cancel each other out again.

f =901.07 Hz

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