Question

A train at rest emits a sound at a frequency of 1045 Hz. An observer in a car travels away from the sound source at a speed of 22.4 m/s. What is the frequency heard by the observer? Assume the speed of sound in air to be 344 m/s. Answer in units of Hz

Answer 1

Answer:976.95Hz

Explanation:

Let $c$ be the speed of sound in medium.

Let $v_{s}$ be the speed of the source.

Let $v_{o}$ be the speed of the observer.

Let $f$ be the frequency emitted by the source when the source is in rest.

Let $f_{new}$ be the frequency observed by the observer.

When the observer is moving away and the source is at rest,

$f_{new}=f\times \dfrac{c-v_{o}}{c}$

Given,

$c=344ms^{-1}$

$v_{s}=0ms^{-1}$

$v_{o}=22.4ms^{-1}$

$f=1045Hz$

$f_{new}=1045\times \frac{344-22.4}{344}=1045\times \frac{321.6}{344}=976.95Hz$