Parametric End‐Fire Array

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...