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 : \[v_s    =    v_b \cos\theta\]

   =\[4\sqrt{2} \times \cos {45}^\circ\]

   =\[4\sqrt{2} \times \frac{1}{\sqrt{2}}   =   4   {\text { ms }}^{- 1}\]

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

\[f = \left( \frac{v}{v  - v_s} \right) f_0 \] 

\[     = \left( \frac{334}{334  - 4} \right) \times 1650\] 

\[     = 1670  \text { Hz }\]