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A sound wave begins traveling through a thin metal rod at one end with a speed...

A sound wave begins traveling through a thin metal rod at one end with a speed that is 15 times the speed of sound in air. If an observer at the other end of the rod hears the sound twice, one from the sound traveling through the rod and one from the sound traveling through the air, with a time delay of 0.12 ?, how long is the rod? The speed of sound in air is 343 ?/?.

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Answer #1

Let's call t1 the time it takes the sound to travel by air from one end of the rod to the other, then:

(where L is the legth of the rod) and t2 the time it takes the sound to travel by the metal from one end of the rod to the other:

We know the difference between the arrival of the sounds is:

Then:

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