First slide

Doppler's effect

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)

Moderate

A

436 to 586
B

426 to 574
C

426 to 584
D

436 to 674

Solution

The linear velocity of Whistle
$v_{S} = rω = 1 .2 \times 2 π \frac{400}{60} = 50 m / s$
When Whistle approaches the listener, heard frequency will be maximum and when listener recedes away, heard frequency will be minimum
So, $n_{\max} = n (\frac{v}{v - v_{s}}) = 500 (\frac{340}{290}) = 586 Hz$
$n_{\min} = n (\frac{v}{v + v_{s}}) = 500 (\frac{340}{390}) = 436 Hz$

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