Answer to Question #88741 in Classical Mechanics for Shivam Nishad

Question

A factory siren has a frequency of 990 Hz.
Calculate the frequency heard by a person
sitting in a car moving at 72 kmh-1 (i) away
from the siren and (ii) towards the siren.
Take the speed of sound in air as 330 ms-1.

Answer 1

Frequency heard by a person differs from factory siren because of doppler effect

$$f=f_0(1+u/c)$$

where $f_0 = 990 \, \text{Hz}$ is factory siren, c = 330 ms-1 is speed of sound, u is the velocity of the receiver relative to the medium.

(i) away from siren $u = - 72 \, \text{km/h} = - 20\, \text{m/s}$ (negative speed means move from source )

$$f = 930 \, \text{Hz}$$

(i)  towards the siren $u = 72 \, \text{km/h} = 20\, \text{m/s}$

$$f = 1050 \, \text{Hz}$$