ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

1aPA4. Influence of phase between original frequencies on the nonlinear generation of new harmonics. Examples of application from nonlinear acoustics.

Claes M. Hedberg

Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063

It is assumed that the solution to a problem is given in the form of a complex multiple Fourier series infinite in each of the original frequencies. In this paper a simple theorem shows that the absolute values of the individual frequency coefficients in the series are independent of the phase relation between the original frequencies. But the coefficients division into real and imaginary parts is phase dependent. When the relation between the frequencies and original phase is not an irrational number, there exists in the sum several coefficients giving the same frequency, and hence the total amplitude for a specific frequency depends on the phase. An example of application is shown resulting from nonlinear acoustics where, e.g., the importance of original phase for parametric arrays can be estimated. [Work supported by TFR, Sweden.]