Experimental Observation of Acoustic Saturation in Water Caused by Nonlinear Propagation Effects

Abstract

If the amplitude of a plane originally sinusoidal wave is high enough, the wave will distort as it propagates, until a sawtooth is formed. Dissipation then slowly smooths the sawtooth. Eventually, at long range, the sinusoidal wave shape is restored. Beyond this range, according to the solution of Burgers's equation, the amplitude of the wave is independent of the source level. In other words, acoustic saturation occurs. In the case of spherical waves, no analytical solution of Burgers's equation is known, but it is possible to estimate the distance at which shocks form and the distance at which the wave loses its sawtooth shape. Curves showing these distances as a function of source level, with frequency as a parameter, have been computed for spherical waves in fresh water. An experiment to investigate the saturation phenomena has been carried out in a fresh-water lake. A piston was used to generate a high-intensity narrow beam at a frequency of 450 kHz. Data was taken along the axis in the farfield. For each range point, a curve of sound-pressure level of the fundamental versus source level has been plotted. Saturation is clearly evident at the longest range (36 yd = 104 wavelengths). The effect of saturation is also seen in the beam patterns, which become blunt at long range as the source level is increased. [This work was sponsored by the U. S. Office of Naval Research.]