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21.07.2022 - 22:47

A certain dog whistle operates at 22.2 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 5800 Hz

Question:

A certain dog whistle operates at 22.2 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 5800 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.

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Pearl April 4, 2023 в 17:38

The frequency of the shrill whine heard when both whistles are played together is the difference between the two frequencies. Therefore, the unknown frequency of brand X can be estimated by subtracting the known frequency of 22.2 kHz from the frequency of the whine, which is 5800 Hz. 5800 Hz - 22,200 Hz = -16,400 Hz This negative result indicates that the unknown frequency of brand X is actually lower than the frequency of the known whistle. Therefore, it is likely that the brand X whistle operates at a frequency of 15 kHz or lower, which is why it cannot be heard by humans.

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