When solving using the method of separation of variables the 1D wave equation 0 x t 0 u z 0 0 u 0 t 0 u x t 0 we assume the solution to the Partial Differential Equation and after substitution we get the two Ordinary Differential Equations O D E s A O D E in space where A is the separation constant The C UE subject to u a 0 2 x 2 P D E as u x t A O D E in time and solution to the problem is therefore u z t A cos A Cos B sint 1 1 and B where A Hint Use pi fort and for the fractional use abc d