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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.

Q.8.    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: Speed of sound in air is  346\ m/s; Speed of sound in aluminium is 6240\ m/s )

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Here, let us assume the length of the rod be 'l'.

Then,

Time taken by the sound wave in air:

\left ( Given: v_{air} = 346\ m/s \right )

Time = \frac{Distance}{Speed}

t_{air} = \frac{l}{346} seconds

Time taken by the sound wave in Aluminium to reach from one end to the other end,

\left ( Given: v_{aluminium} = 6420\ m/s \right )

t_{aluminium} = \frac{l}{6420} seconds

Therefore, the ratio of the time taken by the sound wave in air and in aluminium will be:

\frac{t_{air}}{t_{aluminium}} = \frac{\frac{l}{346}}{\frac{l}{6420}} = \frac{6420}{346} = \frac{18.55}{1}

Hence, the ratio is 18.55:1.

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