A source of sound vibrating at frequency 500\ Hz is rotated in a...

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

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

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

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

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

f_\max = f_0 \left( \dfrac{v}{v - v_s} \right)<br><br>f_\max = 500 \left( \dfrac{332}{332 - 10} \right) =$500 \left( \dfrac{332}{322} \right) \approx$515.5\ $\text{Hz} \approx$516\ $\text{Hz}<br><br>The minimum frequency is heard when$ the source moves directly away from the listener:

f_\min = f_0 \left( \dfrac{v}{v + v_s} \right)$<br><br>$f_\min = 500 \left( \dfrac{332}{332 + 10} \right) = 500 \left( \dfrac{332}{342} \right) \approx 485.3\ \text{Hz} \approx 485\ \text{Hz}$<br><br>Answer:$516\ \text{Hz} and $485\ \text{Hz}$