Question

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 (speed of sound = 340 m/s)

• A. 436 to 586
• B. 426 to 574
• C. 426 to 584
• D. 436 to 674

Answer 1

The correct option is A 436 to 586

$v_s=rw=1.2\times 2\pi \frac{400}{60}=50m/s$
When Whistle approaches the listener, heard frequency will be maximum and when whistle recedes away,heard frequency will be minimum

So, $n_{max}=n\left(\frac{v}{v-v_i}\right)=500\left(\frac{340}{290}\right)=586Hz$
$n_{min}=n\left(\frac{v}{v+v_i}\right)=500\left(\frac{340}{390}\right)=436Hz$