# 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.

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Given:
Two children are at opposite ends of an aluminum rod. One strikes the end of the rod with a stone.

To do:
To find the ratio of times taken by the sound wave in the air and in aluminum to reach the second child.

Solution:

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

Let us use the speed-distance formula:

$\boxed{speed=\frac{distance}{time}}$

Time taken by the sound wave in the air:

Velocity of sound in air $v_{air}=340\ m/s$
$t_1=\frac{d}{v_{air}}=\frac{d}{340}$        .....$(i)$

Time taken by the sound wave in aluminum rod:

Velocity of sound in aluminium rod $v_{rod}=6420\ m/s$
$t_2=\frac{d}{v_{rod}}=\frac{d}{6420}$     .....$(ii)$

Ratio of times taken by the sound wave in the air and in aluminum:
On Dividing $(i)$ and $(ii)$ equations
$\frac{t_1}{t_2}=\frac{6420}{340}=18.88$
Updated on 10-Oct-2022 13:23:15