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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)
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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