Study on phase of reflection coefficient of the medium with gradient change of acoustic impedance

Medium with gradient change of acoustic impedance is a new type acoustic structure which composed of several materials and has a continuous gradient composition and structure whose specific acoustic impedance varies smoothly across the layer. It has been used in various practical situations such as acoustic rectifiers, medical devices, weakening vibration and reducing noise. The purpose of this paper is to investigate the phase characteristics of reflection coefficient of medium with gradient change of impedance to make use of the sound pressure and vibration velocity of the wave. Exact solutions of the Helmholtz equation are derived for a typical density profile and sound-speed profile. The solutions in the medium are matched with solutions in the homogeneous upper and lower layers to derive analytical expressions for the phase of the reflection coefficient of a plane wave which incident from the upper medium. The phase of reflection coefficient in a variety of cases that of different frequencies and incident angles are examined. A number of simulation results are presented and comparison is made with computed results. The phase data can be used in the subsequent vector signal processing.