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A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as `344 ms^(-1)`.

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(i) In the first case:
Speed, `v = 344 ms^(-1)`
Frequency, `f = 20 Hz`
And, Wavelength, `lambda = ?` (To be calculated)
Now, `v = f xx lambda`
So, `344 = 20 xx lambda`
`lambda = (344)/(20)m`
Wavelength, `lambda = 17.2m`...(1)
(ii) In the second case:
Speed, `v = 344 ms^(-1)`
Frequency, `f = 20 kHz`
`= 20 xx 1000 Hz` (Because `1kHz = 1000 Hz)`
`= 20000 Hz`
And, Wavelength, `lambda = ?` (To be calculated)
Now, `v = f xx lambda`
So, `344 = 2000 xx lambda`
`lambda = (344)/(20000)`
Wavelength, `lambda = 0.0172m` ...(2)
Thus, the wavelengths of sound in air corresponding to the frequencies of 20Hz and 20 kHz are 17.2m and 0.0172 m respectively.

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