In this paper, uniqueness of periodic solutions of a certain ultra-hyperbolic boundary value problem was investigated using energy method and superposition principle. Periodic solutions and test for periodicity were obtained using separation of variable method and Fourier series. Through the exploit of energy conservation and initial conditions, uniqueness of periodic solutions were established. Application of our results can be seen in wave propagation and vibration in complex system with periodic forcing. Numerical simulations were used to demonstrate the behavior of the solutions extending known results in literature.