Question

A whistle of frequency 500 Hz tied to the end of a string of length 1.2 m revolves at 400 revolutions per minute. If the velocity of sound is 340 m/sec, a listener standing some distance away in the plane of rotation of the whistle hears the frequencies in the range

• A. 436 to 586 Hz
• B. 426 to 574 Hz
• C. 436 to 574 Hz
• D. 426 to 586 Hz

Answer 1

Answer: (A)

: Velocity of source $v_s=R\omega$ $=R\times 2\pi n$ $=1.2\times 2\times 3.14\times \frac{400}{600}$ = 50 approximately $\therefore$ Maximum apparent frequency $=\frac{vn}{(v-v_s)}$ $=\frac{340\times 500}{(340-50)}=\frac{170000}{290}=586Hz$ Minimum apparent frequency $=\frac{vn}{v+v_s}$ $=\frac{340\times 500}{(340-50)}=\frac{17000}{390}=436Hz$ $\therefore$ Range is 436 to 586 Hz.