The theory presented in two previous papers [J. Acoust. Soc. Am. 74, 1013–1020 (1983) and J. Acoust. Soc. Am. 75, 769–779 (1984)] is generalized to the second harmonic and sum frequency components in the acoustic beam from a moderate amplitude parametric radiator. The theory also applies to the second harmonic component in the acoustic field from a moderate amplitude monochromatic transducer. Asymptotic formulas are presented, showing the development of the second harmonic and sum frequency sound from the source (transducer) into the farfield. Numerical results for the axisymmetric case are given. The results are compared with earlier theories and observations.
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Berntsen et al. (1984) studied this question.