NONLINEAR SOUND GENERATION BY HADRON SHOWERS

Abstract

In connection with Project DUMAND, the proposal to utilize the ocean as a giant acoustic detector of neutrinos, we have studied the applicability of a recent theory of thermoacoustic arrays (Peter J. Westervelt and Richard S. Larson, J. Acoust. Soc. Am. 54 (1973) 121). In the static case or at very low frequencies, about 10 % of the coefficient of thermal expansion for water at 20°C can be attributed to Debye-like modes. Debye-like modes generate sound via the non-linear mechanism responsible for the operation of the parametric acoustic array (Peter J. Westervelt, J. Acoust. Soc. Am. 35 (1963) 535). The contribution of the Debye-like modes to the thermal expansion coefficient, and thus to the sound pressure, is essentially independent of the ambient water temperature. Hence if the Debye-like modes are not fully excited as we postulate to be the case at high frequencies, then the thermal expansion coefficient will be less than the static value by an amount that causes it to vanish at about 6°C instead of at 4°C, the temperature of maximum water density. This theory is in agreement with recent measurements of the temperature dependence of sound generated by proton deposition in water (L. Sulak et al., Proceedings of the La Joll a Workshop on Acoustic Detection of Neutrinos, 25-29 July 1977, Scripps Institute of Oceanography, U.C.L.A., San Diego, Hugh Bradner, Ed.). A further consequence of our work implies that the conventional thermoacoustic theory be modified by subtracting the parametric source terms at high frequencies.