Answer Happy

1. Consider the function Y(x, t) = x² + bxt + t², where b is some constant. The general solution to the wave equation has the form Y(x, t) = f(x-vt) + g(x + vt). By inspection, write down two values of b that would make the given function a wave, and in a. each case give the corresponding velocity. b. Show, by direct substitution of the function into the wave equation itself, that in fact b can be any value and still the function represents a wave. Comment on the wave's velocity. c. Suppose b = 0 so that Y(x, t) = x² + t². By trial and error find a way to express this in the form y(x, t) = f(x − vt) + g(x + vt). The value to use for tv should be clear from the previous part.