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 the distance between the two children be $d$

Also let the time taken by sound to reach other child via air be $t_1$ and via aluminium rod be $t_2$.

Velocity of sound in air $v_a=340$ $m/s$

$\therefore$ $t_1=\frac{d}{v_a}=\frac{d}{340}$ ..........(1)

Velocity of sound in aluminium rod $v_R=6420$ $m/s$

$\therefore$ $t_2=\frac{d}{v_R}=\frac{d}{6420}$ ..........(2)

Dividing equation (1) and (2), we get $\frac{t_1}{t_2}=\frac{6420}{340}=18.88$