A whistle of frequency 500 Hz tied to the end of a string of length 1.2 m revolves at 400 rev/min. A…
A whistle of frequency 500 Hz tied to the end of a string of length 1.2 m revolves at 400 rev/min. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range
(Take, speed of sound = 340 m/s)
436 Hz to 586 Hz
426 Hz to 574 Hz
426 Hz to 584 Hz
436 Hz to 674 Hz
Solution
The linear velocity of whistle,
$v_s = r\omega = 1.2 \times 2\pi \frac{400}{60} = 50 \text{ m/s}$
When whistle approaches the listener, heard frequency will be maximum and when whistle recedes away, heard frequency will be minimum.
So, $f_{\text{max}} = f \left(\frac{v}{v - v_s}\right) = 500 \left(\frac{340}{290}\right) = 586.2 \text{ Hz} \approx 586 \text{ Hz}$
and $f_{\text{min}} = f \left(\frac{v}{v + v_s}\right) = 500 \left(\frac{340}{390}\right) = 435.89 \text{ Hz} \approx 436 \text{ Hz}$