Chapter - 5 Sound

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Q
Sound

Question:

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.

Answer:

Consider the length of the aluminium rod to be D.

The speed of the sound wave in aluminium at 25°C is 6420 m/s.

The speed of the sound wave in the air at 25°C is 346 m/s.

We know,

Speed = frac{Distance}{Time}

Time = frac{Distance}{Speed}

Therefore, time taken by the sound wave to reach the other end in air will be:

t_{air}= frac{D}{346}

And, the time taken by the sound wave to reach the other end in aluminium will be:

t_{Alu}= frac{D}{6420}

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

frac{t_{air}}{t_{Alu}}= frac{frac{D}{346}}{frac{D}{6420}}

frac{t_{air}}{t_{Alu}}= frac{6420}{346}

frac{t_{air}}{t_{Alu}}= 18.55


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