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- A standing wave us given by y(x,t) = 10cos(5(pi)t)*sin((2/3)(pi)x) find two waves that could be superimposed to generate this standing wave.Examine the wave function below. Suppose there is a point that goes from y = 2 mm to y = 6 mm. How long does it take for the point to make the move?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).Another Wave Equation With Damping Determine the specific solution to the wave equation with damping ди(х, 1) Ə²u(x,t) ôx² ô²u(x,t) + 4 for 0 < x < n and 0 < t, given also the BCs: u(0,t) initial conditions O and u(n,t) = 0 for 0 < t and the ôu(x,t) u(х,0) : = x and -0