question_answer

                A whistle revolves in a circle with angular velocity \[\omega =20\] rad/s using a string of length 50 cm. If the actual frequency of sound from the whistle is 385 Hz, then the minimum frequency heard by the observer far away from the centre is : (velocity of sound v = 340 m/s)                                                                              

A)                 385 Hz 

B)                 374 Hz  

C)                 394 Hz         

D)                 333 Hz

Correct Answer: B

Solution :

                 Velocity of source (whistle) is given by                 \[{{v}_{s}}=r\omega \]                 \[=(0.5\,m)\,(20\,rad/s)\]                 \[=10\,m/s\]                 The frequency of sound observed by the observer will be minimum when he is at point A. Thus, at this point minimum frequency of source as observed by observer is                                 \[{{n}_{\min }}=\left( \frac{v}{v+{{v}_{s}}} \right)n\]                 \[{{n}_{\min }}=\frac{340}{340+10}\times 385=\frac{34}{35}\times 385\]                 = 34 × 11 = 374 Hz