Show explicitly that the wave function, y(x, t) = A cos(kx - wt), satisfies the wave equation,

Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.

a pulse traveling along a string of linear mass density μ as a wave function, y(x),  if the power carried by this wave at a point x is described as P(x):                          P (x) = (μ ω3 / k) e πx  1) What is the power P(0) carried by this wave at the origin? 2) Compute the ratio P(x)/P(0).