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

Frequency of Pulse for II Boy is 1670 Hz

Explanation:

• The speed of source u = $4\sqrt 2$ $ms^-^1$.  

Sound Speed V = 334 $ms^-^1$

. The frequency of sound v = 1650 Hz.  

• Since the observer is standing at 45° from the direction of motion, the speed of the source for the observer  

= u cos 45°

= $\frac {u}{\sqrt 2}$

• Hence the apparent frequency received by the second boy-

v' = $\frac {Vv}{(V - u)/\sqrt 2}$

= $\frac {334 \times 1650}{334 - 4}$

= $\frac {334 \times 1650}{330}$

= 1670 Hz

* Refer figure attached