Transient axial solution for the reflection of a spherical acoustic wave from a rigid concave parabolic reflector

摘要

A transient solution is presented for the reflected acoustic wave along the axis of symmetry of a rigid concave parabolic reflector. The incident field is a spherical wave produced at the focus of the reflector. The present solution is applied to a Gaussian modulated sinusoidal pulse. And the evolution of the axial waveform components and the effect of depth-to-focal-length ratio on the peak power density are studied and analyzed. A concept of "diffraction- leading zone" is proposed based on the calculation results. Inside the diffraction-leading zone, increasing the depth-to-focal-length ratio has no effect on improving the peak power density. While out of the diffraction-leading zone, the peak power density will be improved as the depth-to-focal-length ratio increasing to a certain limit at different ranges. If the aperture size of the reflector is fixed, an optimized depth-to-focal-length ratio exists to maximize the gain in the far field.