Question

Hi everyone , I have a problem on physics.

A man strikes one end of a thin rod with a hammer. The speed of sound in the rod is 17 times the speed of sound in air. A woman, at the other end with her ear close to the rod, hears the sound of the blow twice with a 0.16 s interval between; one sound comes through the rod and the other comes through the air alongside the rod. If the speed of sound in air is 347 m/s, what is the length of the rod?

Please don't forget the unit of the answer.

Below is the hint:

In symbols, how much time does the sound take to travel a distance d in air? How much through the same distance in the rod? The speed of sound in the rod is given in terms of the speed in air.

Thamks a lot.

Answer 1

Let the length of rod be 'L' (meters). Now the speed of sound in air is V_air = 347 m/sec and the speed of sound in rod is V_rod = 17*V_air = 17*347 = 5899 m/sec.

So the time taken by sound to reach the woman's ear are (i) through air is t_air = L/V_air = L/347 sec, (ii) through the rod is t_rod = L/V_rod = L/5899 sec, given that the difference in the times is 0.16 sec.

So, (L/347) - (L/5899) = 0.16, implies 0.00288184L - 0.00016952L = 0.16, implies 0.0027123L = 0.16, implies L = 58.99 meters, is the length of the rod.