Determining natural frequencies of oscillation

Question

Assignment:

Consider the displacement of ,u(r,Θ,t) , a "pie-shaped" membrane of radius a and angle π/3that satisfies:

u_tt = c²∇²u

Assume that l>0. Determine the natural frequencies of oscillation if the boundary conditions are:

Problem a.

a) u(r, 0, t) = 0,   u(r, π/3, t) = 0, u_r(a, θ, t) = 0

problem b.

b)    u(r, 0, t) = 0,   u(r, π/3, t) = 0, u(a, θ, t) = 0

Provide complete and step by step solution for the question and show calculations and use formulas.