Establish the relationship between speed of sound, its wavelength and frequency. If velocity of sound in air is 340 m s^-1, calculate
(i) Wavelength when frequency is 256 Hz.

(ii) Frequency when wavelength is 0.85 m.

Question

Philoid · Accepted Answer

Frequency and time period are related as follows: √ = (I)

We know, Speed, v =

v =

Here λ is the wavelength of the sound wave. It is the distance traveled by the sound wave in one time-period (T) of the wave.

Thus,

v = λ√ (From I)

That is, Speed = wavelength * Frequency

The speed of sound remains almost the same for all frequencies in a given medium under the same physical conditions.

(i) Given, Speed (v) = 340 m/s

Frequency (√) = 256 Hz

Wavelength (λ) =?

v = λ√

340 = 256λ

λ = 1.33 m

(ii) Given, Speed (v) = 340 m/s

Wavelength (λ) = 0.85 m

Frequency (√) =?

v = λ√

340 = √ (0.85)

√ = 400 Hz

Establish the relationship between speed of sound, its wavelength and frequency. If velocity of sound in air is 340 m s-1, calculate(i) Wavelength when frequency is 256 Hz.(ii) Frequency when wavelength is 0.85 m.