The Generation of Harmonics by Small Circular Orifices

Abstract

A spectral analysis was made of the sound field emanating from a small orifice set flush in the top of a table which acted as an infinite baffle. The orifice was driven at a single frequency at various intensities by an electromagnetic horn exciter, coupling through a small cavity below the baffle. At high intensities all harmonics up to the fortieth have been detected. Starting at a distance of one radius from the center of the orifice, the fundamental component of the sound pressure is observed to decrease at a rate of six decibels per distance doubled, indicating that the orifice acts as a spherical source whose radius is that of the orifice. The higher harmonic components decay at the same rate as the fundamental indicating that, for the levels considered, essentially no integrative interactions occur between the harmonics while progagating away from the orifice. Thus it appears that harmonic generation occurs locally at the orifice. The successive odd harmonics are invariably stronger than the immediately preceding even harmonics. Even at moderate levels, the third harmonic may lie less than five decibels below the fundamental component. A theory based upon the non-linear wave equation in spherical coordinates has been developed which accounts for the first two harmonics semiquantitatively. No account is taken of turbulence or rotational terms in the theory.