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Question
The audible range of frequencies of an average human ear is from 20 Hz to 20 kHz. Calculate the corresponding wavelengths. (Speed of sound in air is 344 ms–1)
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Solution
We have to calculate the wavelength range of audible sound.
Given: Speed of sound ν = 344 m/s
Lower frequency of audible range fL = 20 Hz
Higher frequency of audible range fH = 20,000 Hz
We know relation of velocity, frequency, and wavelength `lambda = v/f`,
where ν is the velocity, f the frequency, and λ the wavelength.
So, wavelength corresponding to the lower frequency is
`lambda_L = 344/20`
= 17.2 m
So, wavelength corresponding to the higher frequency is
`lambda_H = 344/20000`
= 0.0172 m
Hence , the range of wavelength in audible region is 17.2 m - 0.0172 m
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