A bar with periodically nonuniform material properties is selected as a one-dimensional model of a flat-panel speaker. This paper describes a theoretical approach to the bending waves propagating i n the nonuniform bar. The phase speed of the wave is obtained using perturbation techniques for small amplitude, sinusoidal modulation of the flexural rigidity and mass density. It is shown that the wave speed is decreased due to the nonuniformity of the material properties by the amount proportional to the square of the modulation amplitude. The resonance occurring when the wavelength is half of the period of the material properties is analyzed by the method of multiple scales. It is also shown that the wave speed at the resonance mode is decreased by the amount proportional to the modulation amplitude but the wave of this mode does not propagate far enough due to attenuation