Question

A sound wave of frequency 100 Hz is travelling in air. The speed of sound in air $350m/s^{-1}$. (a) By how much is the phase changed at a given point in $2.5m$? (b) What is the phase difference at a given instant between two points separated by a distance of $10.0cm$ along the direction of propagation?

Answer 1

Given:

$\nu =100Hz$

Speed of sound in air, $V$ = $350m{s}^{-1}$

(a) To find the phase difference at point in 2.5ms

Wavelength, $\lambda =\frac{V}{\nu }=\frac{350}{100}=3.5m$

The distance travelled by the wave in $2.5ms=350\times 2.5\times {10}^{-3}$

Now, Phase difference,

$\varphi =\frac{2\pi }{\lambda }\times △x=\frac{2\pi }{3.5}\times 350\times 2.5\times {10}^{-3}=\frac{\pi }{2}$

(b) To find phase difference between points separated by 10cm

$Here,△x=10cm=0.1m$

$\varphi =\frac{2\pi }{\lambda }\times △x=\frac{2\pi }{3.5}\times 0.1=\frac{2\pi }{35}$