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.At what minimum speed should you ride to know if the whistle is working?

Answer 1

To solve this problem we will apply the concepts related to the Doppler effect. According to this concept, it is understood as the increase or decrease of the frequency of a sound wave when the source that produces it and the person who captures it move away from each other or approach each other. Mathematically this can be described as

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

Here,

$f_0$ = Original frequency

$v_0$ = Velocity of the observer

$v$ = Velocity of the speed

Our values are,

$v = 340m/s \rightarrow \text{Speed of sound}$

$f = 20kHz \rightarrow \text{Apparent frequency}$

$f_0 = 21kHz \rightarrow \text{Original frequency}$

Using the previous equation,

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

Rearrange to find the velocity of the observer

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

Replacing we have that

$v_0= (340m/s)(1-\frac{20kHz}{21kHz})$

$v_0 = 16.19m/s$

Therefore the velocity of the observer is 16.2m/s