Sound propagation from a dipole source near an impedance plane

Abstract

A closed-form analytic solution has been derived for an arbitrarily oriented dipole placed above an impedance plane. Asymptotic approximations for the total sound field can be written in a form similar to the classical formula for a monopole. Analytic approximations derived for horizontal and vertical dipoles give predictions that agree well with those obtained from a program of the fast field type. The asymptotic results have been confirmed also by laboratory measurements. Compared with numerical methods, the analytic approximations offer the combined advantages of easier physical interpretation and a much reduced computational time. It is found that the variation of the sound-pressure level from a vertical dipole above an impedance plane differs significantly from that due to a monopole above this plane, particularly as a result of differences in the ground wave component. However, the excess attenuation due to a horizontal dipole is found to be rather similar to that for a monopole except for source and receiver heights that are comparable with range.