Effective lengths of parametric acoustic sources

Abstract

Computations of effective virtual-source array lengths for parametric acoustic sources are presented. The effective length is defined as the distance from the primary projector where the difference-frequency source level is 1 dB different from (it may be greater or less than) the farfield value. For absorption-limited (i.e., low primary level) sources, the parameter, 2αreff (where α is the primary absorption coefficient and reff is the effective length), is plotted as a function of the single variable, 2αR0f0/f (where R0 is the Rayleigh length, f0 the primary frequency, and f the difference frequency). For 2αR0f0/f≲1, 2αreff∠1/2. For 2αR0f0/f≳1, 2αreff increases by an order of magnitude. As the primary level is increased, the parametric source becomes saturation-limited, and no such simple scaling exists. Results covering a range of useful cases are presented for reff/R0.