Radiation of difference-frequency sound generated by nonlinear interaction in a silicone rubber cylinder

Abstract

In this paper we describe an experimental and theoretical investigation of the parametric signal generated in one medium, a silicone rubber cylinder, and radiated into a second medium, water. The primary waves (∠1.4 MHz) are confined to a narrow region around the axis of the cylinder and, because of the relatively high absorption at these frequencies, are largely attenuated before reaching the end of the cylinder. The silicone rubber cylinder serves two purposes. First, the low sound speed (∠1000 m/sec) and high parameter of nonlinearity (1+B/2A?5) of the silicone rubber makes the virtual sources more than seven times as strong as they would be in water. Second, because the sound speed in silicone rubber is less than that of the surrounding water, the silicone rubber cylinder acts as a slow waveguide antenna for the difference-frequency waves. The system is analyzed by numerically solving the system of equations obtained by coupling the surface Helmholtz integral equation for the interior of the silicone cylinder (which includes the virtual sourcesI with the integral equation for the region exterior to the cylinder. Experimental results obtained for difference frequencies between 10 and 20 kHz compare favorably with theory. Subject Classification: [43]25.35, [43]25.15; [43]30.75.