Question

Obtain the value of the constant c for which the function u(x,t) = cosαcxsinαt is a
solution of the wave equation :
d^2u/dt^2=c^2(d^2u/dx^2)

Answer 1

$$d^2 u/dt^2= - α^2 cosαcxsinαt$$

$$d^2u/dx^2=-α^2c^2cosαcxsinαt$$

Thus,

$$-α^2=c^2(-α^2c^2)\implies c^4=1$$

c=+1 or c=-1