Question

A table is revolving on its axis at $5$ revolution per sec. A sound source of freq. $1000Hz$. is fixed on the table at $70cm$ from the axis. The minimum frequency heard by a listener standing at a distance very far from the table will be (speed of sound $352\text{m/s}$).

• A. $\text{941 Hz}$
• B. $\text{352 Hz}$
• C. $\text{1066 Hz}$
• D. $\text{1000 Hz}$

Answer 1

The correct option is A $\text{941 Hz}$

Given: $r=70\text{cm}$ ,Speed of sound $=352\text{m/s},\nu =5\text{rev/s},f_0=1000\text{Hz}$

Velocity of source is given by,
$v_s=r\omega =r\times \left(2\pi \nu \right)=\frac{70}{100}\times 2\times \frac{22}{7}\times 5$
$v_s=22\text{m/s}$

Minimum frequency is heard by the obserber when the source is going away from it, so,
$f_{min}=f_0\left(\frac{v}{v+v_s}\right)=\frac{352\times 1000}{352+22}$

$\Rightarrow f_{min}=941\text{Hz}$
Hence, option $\left(C\right)$ is correct.