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.

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aristocles aristocles · Answer 1 · 2019-09-15T04:38:42+02:00

Answer:

[tex]f_2 = 18.5 kHz[/tex]

Explanation:

As the two whistle are played simultaneously

we know that we will hear beats in that case

so we can say

[tex]f_{beat} = f_1 - f_2[/tex]

so here we will have

[tex]f_1 = 23.5 kHz[/tex]

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

[tex]f_{beat} = 5000 Hz[/tex]

so the unknown frequency is given as

[tex]f_{beat} = 23.5 kHz - f_2[/tex]

[tex]5000 = 23.5 - f_2[/tex]

[tex]f_2 = 18.5 kHz[/tex]