Question

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

Answer 1

$$\frac{d^2y}{dx^2}=-A\frac{\pi ^2n^2}{l^2}\sin\frac{\pi nx}{l}\cos2πft \\ \frac{d^2y}{dt^2}=A(2\pi f)^2\sin\frac{\pi nx}{l}\cos2πft$$