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

Answer 1

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