Question

(a) Explain the terms 'crests' and 'troughs of a wave? What type of waves consist of crests and troughs?
​(b) The flash of a gun is seen by man 3 seconds before the sound is heard. Calculate the distance of the gun from the man (Speed of sound in air is 332 m/s).

Answer 1

(a) When a wave travels through a medium, the particles of the medium oscillate about their mean position, up and down. The maximum displacement of the particles above the mean position is referred to as a 'Crest' and the maximum displacement below the mean position is referred to as a 'Trough'. All the transverse waves consist of crests and troughs.

(b) Let the distance of the man from the gun = d

Speed of the light = $3\times {10}^8\mathrm{m}/\mathrm{s}$

Speed of the sound = $332\mathrm{m}/\mathrm{s}$

Let the time taken by the sound to reach the man = t = $\frac{d}{332}$ .......(1)

Then the time taken by the light to reach the man = t$-$3 = $\frac{d}{3\times {10}^8}$ ........(2)

Putting the value of 't' from equation (1) into equation (2), we get,

$$\begin{gathered} \frac{d}{332}-3=\frac{d}{3\times {10}^8} \\ \Rightarrow \frac{{\displaystyle d}}{{\displaystyle 332}}-\frac{{\displaystyle d}}{{\displaystyle 3\times {10}^8}}=3 \\ \Rightarrow \left(\frac{3\times {10}^8-332}{3\times {10}^8\times 332}\right)d=3 \\ \Rightarrow (0.003)d=3 \\ \Rightarrow d=1000\mathrm{m} \end{gathered}$$

Hence, the distance of the man from the gun is 1000 m.