Question

A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If humans can hear neither whistle when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.

Answer 1

Answer:

$f_2 = 18.5 kHz$

Explanation:

As the two whistle are played simultaneously

we know that we will hear beats in that case

so we can say

$f_{beat} = f_1 - f_2$

so here we will have

$f_1 = 23.5 kHz$

also we know that the shrill that we feel when both whistle are sounded

$f_{beat} = 5000 Hz$

so the unknown frequency is given as

$f_{beat} = 23.5 kHz - f_2$

$5000 = 23.5 - f_2$

$f_2 = 18.5 kHz$