Question

A boy riding on a bicycle going at 12 km h⁻¹ towards a vertical wall whistles at his dog on the ground. If the frequency of the whistle is 1600 Hz and the speed of sound in air is 330 m s⁻¹, find (a) the frequency of the whistle as received by the wall (b) the frequency of the reflected whistle as received by the boy.

Answer 1

Given:
Velocity of sound in air v = 330 ms⁻¹

(a) Frequency of whistle $n_0$ = 1600 Hz
Velocity of source v_s = 12 km/h = $12\times \frac{5}{18}=\frac{10}{3}{\mathrm{ms}}^{-1}$
Velocity of an observer $v_0$ = 0 ms⁻¹
Frequency of whistle received by wall n = ?
Frequency of sound received by the observer is given by:

$n=\frac{v+v_0}{v-v_s}\times n_0$

On substituting the respective values in the above formula, we get:

$n=\frac{330+0}{330-{\displaystyle \frac{10}{3}}}\times 1600=1616\mathrm{Hz}$
(b) Here,
Velocity of observer $v_0$ = $\frac{10}{3}{\mathrm{ms}}^{-1}$
Velocity of source v_s = 0
Frequency of source $n_0$ = 1616 Hz
Frequency of sound heard by observer is
$n=\frac{v+v_0}{v+v_s}\times n_0$

On substituting the respective values in the above formula, we get:

$=\frac{330+{\displaystyle \frac{10}{3}}}{330+0}\times 1616=1632\mathrm{Hz}$