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

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Detailed Solution

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

18.88

.
Let the distance between the two children be

d .

Also, let the time taken by sound to reach another child via air be

t_{1}

and via aluminium rod be

t_{2}

.
The velocity of sound in air,

v_{a} = 340 m / s

t_{1} = d / v_{a}

= d / 340

----------------

(1)

Velocity of sound in aluminium rod,

v_{r} = 6420 m / s

t_{2} = d / v_{r}

= d / 6420

---------------

(2)

Divide equation

(1)

by equation

(2),

we get

t_{1} / t_{2} = 6420 / 340

= 18.88

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