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Question
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 m s−1.
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Solution
Given:
Speed of sound in air = 344 ms−1
Frequencies in the audio range:
V1 = 20 Hz, V2 = 200
v = vλ
λ = Vv
kHz = 20000 Hz,
(i) Case I: When frequency V1 = 20 Hz.
λ1 = `"v"/"V"_1`
= `(344 "ms"^-1)/(20 "Hz")`
= 17.2 m
(ii) Case II: When frequency V2 = 20,000 Hz.
λ2 = `"V"/"V"_2`
= `(344 "ms"^-1)/(20,000 "Hz")`
= 0.0172 m
So, the wavelength of sound waves for both frequencies is 17.2 m and 0.0172 m, respectively.
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