Waves of Arbitrary Shape.
(a) Explain why any wave described by a function of the form y(x, t) = fix - ut) moves in the +x-direction with speed u.
(b) Show that y(x, t) = f(x - ut) satisfies the wave equation, no matter what the functional form of f to do this, write y(x, t) = f (u), where u = x - ut. Then, to take partial derivatives of y (x, t), use the chain rule:

(c) A wave pulse is described by the function y(x, t) = De -(Bz-Ct)2, where B, C, and D are all positive constants. What is the speed of this wave?

dy(x, t) df(u) au _ df(u) (--) du du at ay(x, t) df(u) du _ df(u) du ax du