Question

In a first experiment, a sinusoidal sound wave is sent through a long tube of air, transporting energy at the average rate of P_avg1. In a second experiment, two other sound waves, identical to the first one, are to be sent simultaneously through the tube with a phase difference phi of either 0, 0.2 wavelength, or 0.5 wavelength between the waves, (a) With only mental calculation, rank those choices of phi according to the average rate at which the waves will transport energy, greatest first, (b) For the first choice of phi, what is the average rate in terms of P_avg1 ?

Answer 1

The phase differences can be ranked in order of their average rate of energy transport. For a phase difference of 0.5 wavelength, the average rate of energy transport is P_avg1/4.

Step-by-step explanation:

In the first experiment, a sinusoidal sound wave is sent through a long tube of air, transporting energy at the average rate of P_avg1.

In the second experiment, two other sound waves, identical to the first one, are sent simultaneously through the tube with different phase differences.

(a) The phase differences can be ranked from greatest to least average rate of energy transport as follows: 0.5 wavelength, 0.2 wavelength, and 0 wavelength.

(b) For the first choice of phi (0.5 wavelength), the average rate of energy transport in terms of P_avg1 would be P_avg1/4.