Question

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A train worker hits a subway rail with a metal hammer. You are standing `Δx = 86` meters down the track from him while he does this. You hear two different sounds. One from the sound as it passes through the metal and the other `187` milliseconds later after the same initial vibrations pass through the air. What is the speed of sound in the metal track?

Answer 1

Clearly this 187 milliseconds difference were created between the two sounds because sound travels faster through metal,

Let,velocity of sound through metal is `v m/s` ,so to travel `delta x` distance it will take time `t= (deltax)/v`

And, if velocity of sound in air is `v' m/s` then similarly we can write,required time is `t' = (delta x)/(v')`

Given, `t'-t=187*10^-3`

So, `delta x(1/(v')- 1/v) = 187*10^-3`

Now,speed of sound in air is about `346 m/s`

so, solving we get, `v'=1388.89 m/s`