A table is revolving on its axis at $5\text{ revolutions per second}$. A sound source of frequency…
A table is revolving on its axis at $5\text{ revolutions per second}$. A sound source of frequency $1000\text{ Hz}$ is fixed on the table at $70\text{ cm}$ from the axis. The minimum frequency heard by a listener standing at a distance very far from the table will be (speed of sound $= 352\text{ ms}^{-1}$)
1000 Hz
1066 Hz
941 Hz
352 Hz
Solution
For source, $v_s = r \omega = 0.70 \times 2\pi \times 5 = 22\text{ ms}^{-1}$
Minimum frequency is heard when the source is receding the man. It is given by $f_{\min} = f \left( \frac{v}{v + v_s} \right) = 1000 \times \left( \frac{352}{352 + 22} \right) = 941\text{ Hz}$