(a) Explain why any wave described by a function of the form y(x,t)= f(x-vt) moves in the +x direction with speed v. (b) Show that y(x,t) = f(x-vt) satisfies the wave equation no matter what the functional form of f. Hint: To do this, write y(x,t) = f(u), where u = x-vt. 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-(Bx-Ct)^2, where B,C, and D are all positive constants. What is the speed of this wave?

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