Question

A boy riding on his bike is going towards east at a speed of 4√2 m s⁻¹. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of 334 m s⁻¹. A second boy stands on the ground 45° south of east from his. Find the frequency of the pulse as received by the second boy.

Answer 1

Given:
Frequency of pulse produced by the bike $f_0$ = 1650 Hz
Velocity of bike $v_b$ = 4$\sqrt{2}$ ms⁻¹
Velocity of sound in air v = 334 ms⁻¹
Frequency of pulse received by the second boy $f$ = ?
Velocity of an observer $v_0$ = 0
Velocity of source will be:
$v_{\mathrm{s}}=v_b\cos \theta$

= $4\sqrt{2}\times \cos {45}^{°}$
= $4\sqrt{2}\times \frac{1}{\sqrt{2}}=4{\mathrm{ms}}^{-1}$

Frequency of pulse received by the second boy is given by:

$$\begin{gathered} f=\left(\frac{v}{v-v_s}\right)f_0 \\ =\left(\frac{334}{334-4}\right)\times 1650 \\ =1670\mathrm{Hz} \end{gathered}$$