Question

Show that the equation y=2Asin(nπx/L)cos2πft for a standing wave is a solution of the wave equation

Answer 1

$$\frac{d^2y}{dx^2}=-A\frac{n^2π^2}{L^2}\sin\frac{nπx}{L}\cos2πft\\ \frac{d^2y}{dt^2}=A(2πf)^2\sin\frac{nπx}{L}\cos2πft$$