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# 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.

__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

$\frac{t_1}{t_2}=\frac{6420}{340}=18.88$

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