Question

Please show all steps for the proofs. I'm having trouble wrapping my heads around these.

15.65CALC Waves of Arbitrary Shape. (a) Explain why any wave described by a function of the form y(x, )f(x - ) hat when moves in the tx-direction with speed u. (b) Show that y(x,1) =f(x-v) satisfies the wave equation, no matter what he figure? the functional form of f. To do this, write y(x, rf(), where harp (fre- power P(x, r) 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, ). In particular, explain what is happening at points where P-0, where there is no instantaneous energy transfer. (c) The quantity P(x, 1) always has the same sign. What does this impl;y about the direction of energy flow? (d) Consider a wave moving in the-x-direction, for which y(x, t) = Acos(kx + ω). Calculate P(x, t) for this wave, and make a graph of y(x, ) and P(x, r) as functions of x for a given time (say,0). What differences arise from reversing the direction of the wave? the t is

Answer 1