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A person has a hearing range from 20 Hz ...

A person has a hearing range from `20 Hz` to `20 kHz`. What are the typical wavelength of sound waves in sir corresponding to these two frequencies ? Take the speed of sound in air as `344 m//s`.

Text Solution

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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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