The orthonormal sets of functions known as Gaussian–Laguerre and Gaussian–Hermite functions (G–L/H) have previously been used in quantum mechanics, electromagnetic waves and laser optics. These functions satisfy a modified wave equation, valid under certain restrictive conditions appropriate to slowly diverging sound fields. The nearfield of an ultrasonic transducer can be expressed as a linear combination of modes, each described by a G–L/H function. Each mode has a slightly different phase velocity in the nearfield but has the same spreading nature and phase velocity in the farfield. Using this formulation, the transition from nearfield to farfield is readily explained.Subject Classification: [43]20.55; [43]35.80; [43]20.15.