Physics - Sound Wave Question with Solution | TestHub

Given frequency of the source, $f_0=500\text{Hz}$

Radius of the circular path, $R=\frac{100}{\pi }\text{cm}=\frac{1}{\pi }\text{m}$

Angular speed, $\omega =5\text{rev/s}=5\times 2\pi \text{rad/s}=10\pi \text{rad/s}$

Linear speed of the source, $v_s=R\omega =\left(\frac{1}{\pi }\right)(10\pi )=10\text{m/s}$

The maximum frequency is heard when the source moves directly towards the listener:

$f_{max}=f_0\left(\frac{v}{v-v_s}\right)$

$f_{max}=500\left(\frac{332}{332-10}\right)=500\left(\frac{332}{322}\right)\approx 515.5\text{Hz}\approx 516\text{Hz}$

The minimum frequency is heard when the source moves directly away from the listener:

$f_{min}=f_0\left(\frac{v}{v+v_s}\right)$

$f_{min}=500\left(\frac{332}{332+10}\right)=500\left(\frac{332}{342}\right)\approx 485.3\text{Hz}\approx 485\text{Hz}$

Answer: $516\text{Hz}$ and $485\text{Hz}$