Consider an infinitely long continuous string with tension . A mass M is attached to the string

Consider an infinitely long continuous string with tension τ. A mass M is attached to the string at x = 0. If a wave train with velocity w/k is incident from the left, show that reflection and transmission occur at x = 0 and that the coefficients R and T are given by R = sin2 θ, T = cos2 θ where tan θ = Mw2/2kt Consider carefully the boundary condition on the derivatives of the wave function at x = 0. What are the phase changes for the reflected and transmitted waves?