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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.
Solution
Vair = 346 m s−1 (at 25°C)
VAI = 6420 m s−1 (at 25°C)
Let the length of the pipe = lm.
Time taken by sound to travel from one child to another through air (t1) = `"Distance"/"Speed"`
t1 = `"l"/346 "s"` ...(i)
Similarly, the time taken by sound to travel from one child to another through aluminium:
t2 = `"l"/6420 "s"` ...(ii)
Equation From (i) and (ii)
`t_1/t_2` = `1/346 ÷ 1/6420`
= `"l"/346 xx 6420/"l"`
= `6420/346`
= `18.55/1`
`t_1 : t_2` = `18.55 : 1`
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