Question: A string is stretched along the x-axis, fixed at each end, and then set into vibration. It is shown in physics that the displacement y = y(x,t) of the point of the string at location x at time t satisfies the one-dimensional wave equation d ² y/dt ² = a ² (d ² y/dx ² ) where the constant a depends on the density and tension of the string. Show that the following functions satisfy the one-dimensional wave equation: (a) y = sin(x+at); (b) y = cos3h[x-at]); (c) y = sinkxcoskat (k is constant)

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