The nonscattering of sound by sound.

A recent claim [D. H. Trivett and P. H. Rogers, J. Acoust. Soc. Am. 71, 1114-1117 (1982)] that a cw plane wave is scattered by a pulse is subject to the same criticism [P. J. Westervelt, J. Acoust. Soc. Am. 29, 199-203, 934-935 (1957) and M. L. Lighthill, Math. Revs. 19, 915-916 (1958)] leveled at an earlier claim [U. Ingard and D. C. Pridmore-Brown, J. Acoust. Soc. Am. 28, 367-369 (1956)] that scattering occurs from the interaction region of two cw sound beams. The pulse wavefunction employed by Trivett and Rogers does not satisfy the homogeneous wave equation, a fact which gives rise to spurious sources responsible for their nonzero result. The correct result is approximated by Esq. (2t) or Eq. (22) [P. J. Westervelt, J. Acoust. Soc. Am. 59, 760-764 (1976)] multiplied by the longitudinal and transverse taper factors of the pulse. At θ = 0 when the pulse and the cw wave are travelling in the same direction, this solution has an infinite directivity index indicating that the scattered wave never levels the interaction region; this situation, unachievable in practice, should not be called a parametric array and contradicts recent results [D. H. Trivett and P. H. Rogers, J. Acoust. Soc. Am. Suppl. 1 72, S40 (1982)]. About thirty years ago I repeated Ingard and Pridmore-Brown's experiment using their apparatus and convinced myself that nonlinearities in the electrostatic transducer were responsible for their nonzero results. [ABSTRACT FROM AUTHOR]