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Steady state unfocused circular aperture beam patterns in nonattenuating and attenuating fluids.

Single integral approximate formulas have been derived for the axial and lateral pressure magnitudes in the beam pattern of steady state unfocused circular flat piston sources radiating into nonattenuating and attenuating fluids. The nonattenuating formulas are shown to be highly accurate at shallow beam depths if a normalized form of the beam pattern is utilized. The axial depth of the beginning of the nonattenuated beam pattern far field is found to be at 6.41Y0. It is demonstrated that the nonattenuated lateral beam profile is represented at this and deeper depths by a Jinc function directivity term. Values of alpha and z are found that permit the attenuated axial pressure to be represented by a plane wave multiplicative attenuation factor. This knowledge should aid in the experimental design of high accuracy attenuation measurements. The shifts in depth of the principal axial pressure maxima and minima due to fluid attenuation are derived. Single integral approximate equations for the attenuated full beam pattern pressure are presented using complex Bessel functions.