Question

A fire engine is moving south at 35 m/s while blowing its siren at a frequency of 400 Hz.

Answer 1

To solve this problem we will apply the concepts related to the Doppler effect. The Doppler effect is the change in the perceived frequency of any wave movement when the emitter, or focus of waves, and the receiver, or observer, move relative to each other. Mathematically it can be described as

$f_d= f_s \frac{(v+v_d)}{(v-v_s)}$

Here,

$f_d$=frequency received by detector

$f_s$=frequency of wave emitted by source

$v_d$=velocity of detector

$v_s$=velocity of source

v=velocity of sound wave

Replacing we have that,

$f_d = 400(\frac{(343+18)}{(343-35)})$

$f_d=422 Hz$

Therefore the frequencty that will hear the passengers is 422Hz