Question

A train is traveling at 30.0 m/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 Hz .

The speed of sound in air should be taken as 344 m/s .

Part A

What frequency fapproach is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it?

Express your answer in hertz.

Part B

What frequency frecede is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

Express your answer in hertz.

Answer 1

Answer:

Part A: 302.05Hz

Part B: 272.01Hz

Explanation: The question is a demonstration of the term called Doppler effect in sounds. Doppler effect could be defined as the variation in the frequency of sound waves between the source of the sound and the receiver due to a relative motion between the source and the receiver.

Let the velocity of sound in air be v, the frequency sensed by a receiver when there is a relative motion between the source and the receiver is given by $f_{o}=f(v+v_{o})/v-v_{s}$ if the receiver is approaching the source and $f_{o}=f(v-v_{o})/v-v_{s}$ if the receiver is receding from the source.

where $f_{o}$ is the frequency perceived by the receiver, $v_{o}$ is the velocity of the receiver, $f$ is the actual frequency of sound produced by the source and $v_{s}$ is the velocity of the source.

$f=262Hz\\v=344m/s\\v_{s}=30m/s\\v_{o}=18m/s$

Part A: receiver is approaching source

$f_{o}=262(344+18)/344-30\\f_{o}=262(362)/314\\f_{o}=302.05Hz$

Part B: receiver is receding from source

$f_{o}=262(344-18)/344-30\\f_{o}=262(326)/314\\f_{o}=272.01Hz$