Question

A whistle you use to call your hunting dog has a frequency of 21 kHz, but your dog is ignoring it. You suspect the whistle may not be working, but you can’t hear sounds above 20 kHz. To test it, you ask a friend to blow the whistle, then you hop on your bicycle. In which direction should you ride (toward or away from your friend) and at what minimum speed to know if the whistle is working?

Answer 1

The Doppler effect is the right concept to solve this problem. The Doppler effect is understood as the change in apparent frequency of a wave produced by the relative movement of the source with respect to its observer. Mathematically it can be described as,

$f = (1-\frac{v_0}{v})f_0$

Here,

$f_0$ = Frequency of the sound from the Whistle

f = Frequency of sound heard

v = Speed of the sound in the Air

Replacing we have that

$1- \frac{v_0}{343} = \frac{20kHz}{21kHz}$

$\frac{v_0}{343} = 1-\frac{20}{21}$

$\frac{v_0}{343} = \frac{1}{21}$

$v_0 = \frac{1}{21}(343)$

$v_0 = 16.33m/s$

Therefore the minimum speed to know if the whistle is working is 16.33m/s