please help me to solve part B only

3 (25 points). (a) Prove that the function u(x,t) = sin(7x) cos(47t) is the solution of the wave equation with the specified initial-boundary conditions. Un = 16ucrs (0.1) u(x,0) = sin(TX), r [, 1] u1(x,0) = 0, re [0,1] u(0,t) = 0, te [0,1] u(1,t) = 0, te [0, 1] (b) Give the finite difference method for the initial-boundary value prob- lems in (a), use Matlab's mesh command to plot the solution of the finite difference method with h = 0.05, At = h/c