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A form of Burgers’ equation is used to derive an algorithm for calculating harmonic generation by a continuous plane wave of ultrasound propagating in a nonlinear, lossy, nondispersive medium. The algorithm accounts for attenuation that is not quadratically related to the frequency of the wave. Attenuation strongly affects the rate of harmonic production. The effect of variations of the relationship between attenuation and frequency is shown. Biological tissue is an example of a highly lossy medium where the attenuation does not increase with the square of the frequency. Calculations for several types of tissue and biological fluids are presented that show, for certain conditions, finite amplitude distortion is possible.

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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.