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  • 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.

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.

Answers (1)

The wavelength of any sound is defined as distance travelled by disturbance in one time period of the oscillation of particle.

\lambda=V \times T

The number of oscillations per unit time is called frequency. Hence, frequency and time period are related as.

f=\frac{1}{T}

By putting the value of time period in the relation of wavelength, we will get:

\lambda =\frac{V}{f}\Rightarrow V=f \times \lambda

i) If frequency and sound velocity is given, wavelength can be calculated as:

\lambda =\frac{V}{f}\\ \Rightarrow \lambda =\frac{340}{256}=1.328125m

ii) If wavelength and sound velocity is given, frequency of sound can be calculated as:

f=\frac{V}{\lambda }\\ \Rightarrow f =\frac{340}{0.85}=400Hz

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