Question

A whistle of frequency $500Hz$ tied to the end of a string of length $1.2m$ revolves at $400rev/min$. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range $(v=340m/s)$

• A. 486 to 586 Hz
• B. 436 to 586 Hz
• C. 436 to 574 Hz
• D. 445 to 570 Hz

Answer 1

The correct option is B 436 to 586 Hz

$\omega =\frac{2\pi N}{60}=41.87rad$, $r=1.2m,v=340m/s$

Now the velocity of whistle will be, $v_1=\omega r=50.24$

Now this velocity at two end of circle will be, $v_1,-v_1$

With an observer stationary relative to the medium, if a moving source is emitting waves with an actual frequency $f=500Hz$.

The observer detects waves with a frequency $f$ given by:

$f_{min}=\frac{vf}{v+v_1}=436Hz$

$f_{max}=\frac{vf}{v-v_1}=586Hz$