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Question
Establish the relationship between the speed of sound, its wavelength and frequency. If the velocity of sound in air is 340 m s–1, calculate
(i) wavelength when the frequency is 256 Hz.
(ii) frequency when the wavelength is 0.85 m
Solution
Speed of sound is the distance travelled by the sound wave per unit time.
Distance travelled by sound wave in periodic time (T) = wavelength (λ) of the sound wave.
Thus, speed of sound, v = `"distance(λ)"/("time taken (T)")`
or v = `λ/"T"`
∵ frequency, v = `1/"T"`
thus v = u
The velocity of sound in air, v = 340 ms−1
(i) Frequency, u = 256 Hz
∴ The wavelength, λ = `"v"/"v" = 340/256 "m"`
= 1.33 M
(ii) Wavelength, λ = 0.85 m
∴ Frequency v = `"v"/λ = 340/0.85 "Hz"`
= 400 Hz
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