NONLINEAR PROPAGATION THROUGH A FLUID OF WAVES ORIGINATING FROM A BIHARMONIC SOUND SOURCE

A sufficiently strong sound source generates in a thermoviscous fluid, due to nonlinearity, a frequency spectrum consisting of all multiples of the original frequencies and the sums and differences of these mul tiples. After a certain distance, a shock front is formed because of t he energy transfer from lower to higher frequencies. In the case of tw o original frequencies as a source (the biharmonic case), the damping of high frequencies leaves us at a large distance from the source with primarily the difference frequency. The propagation of plane waves is described by the Burgers' equation whose solution in the regions befo re and after the shock formation exhibits significantly different appr oximate analytical expressions. In this work, an analytical descriptio n of the total amplitude in the region after formation of shock in the case of a biharmonic sound source is found. This is a generalization of the well-known Khokhlov solution for a monochromatic (single freque ncy) source. This description is turned into a Fourier series which ca n be specialized into the classical Fay solution for a monochromatic s ource. From this Fourier series the behavior of the individual frequen cies is obtained, in particular the difference frequency which is also examined.