Question

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

Answer 1

Step 1: Given data

speed of sound $v_{}=340m/s$

Let the distance between the two children be d and let the time taken by sound to each other child via air be $t_1$ and via aluminum rod be $t_2$.

Step 2: To find the ratio of times taken by the sound wave in the air and in aluminum

The velocity of sound in air $v_a=340m/s$

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

The velocity of sound in aluminum rod $v_r=6420m/s$

$t_2=\frac{d}{v_r}=\frac{d}{6420}............\left(2\right)$

Dividing equations 1 and 2

$\frac{t_1}{t_2}=\frac{6420}{340}=\frac{321}{17}$.

Thus, the ratio of times taken by the sound wave in the air and in aluminum to reach the second child is $321:17$.