Reflection of a spherical sound wave by an infinite elastic plate with an air-back cavity

In this paper, the reflection of a spherical sound wave by an infinite elastic plate with an air-back cavity is theoretically investigated. A far-field expression in closed form for the reflected sound field which includes the effects of the plate vibration excited by the surrounding sound field is derived analytically. The energy ratio of the reflected sound wave by an infinite elastic plate to that by an infinite rigid immovable plate is defined. The ratio is found to take the same form as the energy reflection coefficient of an air-cavity backed infinite elastic plate which the authors have previously derived in the case of a plane wave incidence. This is to say that the effects of the parameters relating to the sound reflecting system should appear in the same manner as in the case of plane wave incidence. The effects of the cavity on the sound reflectivity, which is a dip due to the resonance of mass-spring system consisting of the plate and the cavity and dips due to the acoustic resonance of the cavity, are discussed in detail.