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 =\[12 \times \frac{5}{18} = \frac{10}{3}   {\text { ms }}^{- 1}\]

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 :

\[n = \frac{330 + 0}{330 - \frac{10}{3}} \times 1600 = 1616 \text{ Hz }\]

(b) Here,
 Velocity of observer \[v_0\] \[\frac{10}{3}   {\text { ms }}^{- 1}\]

 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 :

\[= \frac{330 + \frac{10}{3}}{330 + 0} \times 1616 = 1632 \text{ Hz }\]