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Chapter 12: Q47P (page 328)

Question: (I) 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.

Short Answer

Expert verified

The operating frequency of brand X is \(28.5\;{\rm{kHz}}\).

Step by step solution

01

Determination of the operating frequency

The operating frequency of brand X value can be obtained by using the beat frequency formula, which is equal to the difference of two different wave frequencies.

02

Given information

Given data:

The frequency of dog whistle is \({f_1} = 23.5\;{\rm{kHz}}\).

The beat frequency is \({f_B} = 5000\;{\rm{Hz}}\).

03

Evaluation of operating frequency of brand X

The operating frequency of brand X can be calculated as:

\(\begin{array}{c}{f_B} = \left| {{f_2} - {f_1}} \right|\\\left( {5000\;{\rm{Hz}} \times \frac{{{{10}^{ - 3}}\;{\rm{kHz}}}}{{1\;{\rm{Hz}}}}} \right) = \left| {{f_2} - \left( {23.5\;{\rm{kHz}}} \right)} \right|\\{f_2} = 28.5\;{\rm{kHz}}\end{array}\)

Thus, the operating frequency of brand X is \(28.5\;{\rm{kHz}}\).

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