Question

(a) Explain the terms 'compressions' and 'rarefactions' of a wave. What type of waves consist of compressions and rarefactions.
(b) A worker lives at a distance of 1.32 km from the factory. If the speed of sound in air be 330 m/s, how much time will the sound of factory siren take to reach the worker?

Answer 1

(a) A longitudinal wave consists of successive compression and rarefaction that is formed due to continuous to and fro motion of a vibrating object.
A compression is that part of a longitudinal wave in which the particles of the medium are closer to one another than they normally are, and there is an instantaneous reduction in the volume of the medium. This is the region of high pressure and density.
A rarefaction is that part of a longitudinal wave in which the particles of the medium are farther apart than normal, and there is an instantaneous increase in the volume of the medium. This is a region of low pressure and density.

(b) We have to calculate the time taken by the sound wave to reach the observer.
Given: Velocity of sound ν = 330 m/s
Distance between the observer and the source d = 1,320 m.
We know, $\mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}}$
Therefore, time taken by the sound wave to reach the observer is
$$\begin{gathered} =\frac{1320}{330}\mathrm{s} \\ =4\mathrm{s} \end{gathered}$$
So, the time taken is 4 s.