Question

A metal rod rests on supports in a tank of water. A sound pulse, of some initial intensity, is generated at one end of the rod. Assume that the sound cannot leave the rod except as a result of partial reflections at its ends; and that there is no loss of intensity otherwise. After 1 round trips, the pulse travels back along the rod for a second round trip. How many end-reflections have occurred? Answer is: 2

If the acoustic impedance of the metal is 3.35×10⁷ Pa·s/m, what fraction of the initial intensity remains at the start of this second round trip?

Answer 1

(a)

we know that,

the sound is generated at one end, it travels along the rod and hits the other end.

after hitting the other end, it is reflected and bounces back to the original end.

in given problem, after 2 round trips, the pulse travels back along the rod for a third round trip.

thus 4 end reflections have occurred.

(b)

fraction of the initial intensity remains at the start of third round trip-

fraction remaining after completing 4 reflections = ^4

= ( - 1 / + 1)^2

= m / w

where m = acoustic impedence of metal

w = acoustic impedence of water = 1.48*10^6 Pa.s/m

= 3.35*10^7 / 1.48*10^6 = 22.6

fraction = ((22.6 - 1 / 22.6 + 1)^2)^4

fraction = 0.49