Question

Two children are at opposite ends of an aluminium rod. One strikes the end of the rod with a stone. Find the ratio of times taken by the sound wave in air and in aluminium to reach the second child.

Answer 1

Let's consider the length of the aluminum rod as d.
The speed of the sound wave at 25°C in aluminum (_V Al_​) is 6420 m/s.
The time taken for the sound wave to reach the other end of the aluminum rod is given by:

_T Al _​= $\frac{d}{V_{Al}​}$​ = $\frac{d}{6420}$​

The speed of sound in air (_V air_​) is 346 m/s.
The time taken by sound to reach the other end through air is given by:

_T air _​= $\frac{d}{V_{air}}​$​ = $\frac{d}{346}$​

Therefore, the ratio of the time taken by sound in aluminum to the time taken in air is:

$\frac{T_{Al}}{​T_{air}}$​​ = $\frac{6420}{346}$ ​= 18.55