Question

A man is holding a sound source at the top of a tower, whicj emits sound of frequency $1000\text{Hz}$. Suddenly. it slips from his hand and falls down with acceleration $g$. The frequency of sound heard by the man at $t=4\text{sec}$ is:

[Velocity of sound in still air $=320\text{m/s},g=10{\text{m/s}}^2$]

• A. $888\text{Hz}$
• B. $444\text{Hz}$
• C. $1632\text{Hz}$
• D. $622\text{Hz}$

Answer 1

The correct option is A $888\text{Hz}$

Given, frequency heard when source is at rest, $f_0=1000\text{Hz}$

Velocity of sound in still air $=320\text{m/s}$
Velocity of observer, $v_o=0$
Velocity of source at $t=4\text{sec}$ is given by
$v_s=u_s+at=0+10\times 4=40{\text{ms}}^{-1}$

Hence, apparent frequency heard by the man at $t=4\text{sec}$:
$f^{\prime }=\left(\frac{v}{v+v_s}\right)f_0$
[since source is moving away from observer]

$\Rightarrow f^{\prime }=\left(\frac{320}{320+40}\right)1000$
$\Rightarrow f^{\prime }=\frac{320}{360}\times 1000$
$\therefore f^{\prime }\approx 888\text{Hz}$