Instantaneous Power in a Wave.
(a) Graph y(x, t) as given by Eq. (15.7) as a function of x for a given time r (say, t = 0). On the same axes, make a graph of the instantaneous power p(x, t) as given by Eq. (15.23).
(b) Explain the connection between the slope of the graph of y(x, t) versus x and the value of p(x, t). In particular, explain what is happening at points where P = 0, where there is no instantaneous energy transfer.
(c) The quantity P(x, t) always has the same sign. What does this imply about the direction of energy flow?
(d) Consider a wave moving in the -x-direction, for which y(x, t) = Acos (kr + "'t). Calculate
P(x, t) for this wave, and make a graph of y(x, t) and p(x, t) as functions of x for a given time t (say, t = 0). What differences arise from reversing the direction of the wave?