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

Answer:

a) Ф = 0

b)  P_avg=2*P_avg,1

Explanation:

Givens:

The phase difference is 0, 0.2λ, or 0.5λ  between the waves.  

Part a:  

since the amplitude of the wave is directly proportional to the average rate so that the waves will transport greater energy when Ф = 0  

Part b:  

The two waves are identical to the first wave, the net amplitude is twice the first waves and the travel in the same tube thus

P_avg=2*P_avg,1