Parametric End-Fire Array

Abstract

A high-power modulated sound beam acts like an end-fire directional array for the modulation frequency. This occurs because the nonlinear terms in the equations of motion cause such a beam to act like a distribution of sources for the modulation frequency. If the sound beam is unmodulated, it behaves precisely like a parametric amplifier for any sound traveling in the direction of beam and thus can be used as a highly directional receiver. In order to test this concept, two carrier beams having approximately the same frequency ω1 ≈ ω2 ≈ ω were superposed on each other. The modulation frequency is then the difference ω8 = /ω1 − ω2/. If the pressure of each carrier is the same and equal to P0 the modulation percentage will be 100. The expression for the radiated intensity Is at a distance R0 far from this source is Is=ωs4P04S02[1 + 12ρ0c0−1(d2p/dρ2)]22(8π)2ρ03C09R02 × 1α2 + k2sin4(θ/2) in which S0 is the cross-sectional area of the carrier beam, α is the pressure attenuation coefficient for the carrier beam, θ is the angle measured from the axis of the carrier beam, and k = ω8/c0. Maximum radiation occurs at θ = 0 in the forward direction of the carrier. Experiments, described in an accompanying paper, agree well with the theoretical expression which, incidentally, shows the same angular dependence as Rutherford scattering in atomic theory. (Supported by the Office of Naval Research.)