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.

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Solution

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 = $12 \times \frac{5}{18} = \frac{10}{3} {ms}^{- 1}$
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:

$n = \frac{330 + 0}{330 - \frac{10}{3}} \times 1600 = 1616 Hz$
(b) Here,
Velocity of observer $v_{0}$ = $\frac{10}{3} {ms}^{- 1}$
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:

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

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