Diffraction of Plane Acoustic Pulses by Obstacles of Arbitrary Cross Section with an Impedance Boundary Condition

Abstract

The diffraction of an arbitrary acoustic pulse by an arbitrary scattering obstacle with an impedance boundary condition is treated by the same techniques used by the author in previous diffraction studies [e.g., “Diffraction of Acoustic Pulses by Obstacles of Arbitrary Shape with a Robin Boundary Condition,” J. Acoust. Soc. Am., 41, 855–859 (1967)]. The problem is formulated as an integrodifferential equation on surface values of pressure or velocity; this equation is then solved numerically for the specific geometry of a long cylinder of square cross section struck laterally by a step pulse in pressure. A useful economy is that the coefficients used in the approximation are independent of the boundary condition and are identical to those used for previous studies involving the same geometry. Results indicate that the surface pressure decreases from the rigid body solution for infinite impedance to an almost constant level for the boundary impedance equal to the fluid impedance.