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