Question

Establish the relationship between speed of sound, its wavelength and frequency. Velocity of sound in air is $340m/s^{-1}$. Calculate frequency when wavelength is $0.85m$.

Answer 1

The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit time.

We know,

speed, $v=distance/time$

$v=\frac{\lambda }{T}$

Here $\lambda$ is the wavelength of the sound wave. It is the distance traveled by the sound wave in one time period $\left(T\right)$ of the wave. Thus,

$v=\lambda f$

where $f=$ frequency

$f=\frac{1}{T}$

Given,

Speed of sound in air, $v=340m/s$

Wavelength, $\lambda =0.85m$

$v=\lambda f$

$⟹f=\frac{v}{\lambda }$

$f=\frac{340}{0.85}$

$f=400Hz$