Question

A sinusoidal wave is sent along a cord under tension, transporting energy at the average rate of Pavg,1. Two waves, identical to that first one, are then to be sent along the cord with a phase difference φ of either 0, 0.2 wavelength, or 0.5 wavelength.

1) With only mental calculation, rank those choices of φ according to the average rate at which the waves will transport energy, greatest first.

2) For the first choice of φ, what is the average rate in terms of Pavg,1?

Answer 1

(1) If the path difference is then the interference is fully destructive.

So, at 0.2 wavelength waves will transport maximum energy,

(2) The amplitude of the resulting wave

....................................................(1)

for the first choice of

so,

from equation (1)

since P is proportional to square of amplitude,

So,

   since,