The Correlation of Non-Linear Resistance, Flow Resistance, and Differential Resistance for Sharp-Edged Circular Orifices

Abstract

According to Sivian's analysis of the acoustic resistance of small orifices a close correlation should exist between three kinds of measurable resistance in small orifices. If the losses are mainly due to the kinetic energy acquired by the air in the orifice the non-linear acoustic resistance RN, the analogous flow resistance RF, and the analogous differential resistance RD, are related thus: RN = 12RF, RD = 2RF. The non-linear acoustic resistance RN of orifices of 0.375 cm and 0.50 cm diameter has been obtained from plane wave transmission loss measurements made in a three-inch tube equipped with a ρc termination. Orifice thicknesses were varied from 0.05 to 1.25 cm. In this manner RN was measurable at incident pressures greater than that required to cause a deviation from constancy in the transmission loss. It was found that, in the non-linear region, the sound pressure of the wave transmitted by the orifice depends on the square of the incident sound pressure. This relation has been verified for incident sound pressure levels ranging from 115 to 160 decibels, and for frequencies from 238 to 800 c.p.s. (All levels considered were well into Region 4 of Ingaard's “phase diagrams.”) Analogous flow resistance measurements have been made on the same orifices for average particle velocities from 100 to 1,600 cm/sec. The analogous flow resistance was found to be given, within ± 30 percent, by a formula derived by Sivian from kinetic energy considerations. In most cases RN was found to be 25 percent greater than RF/2, and essentially independent of frequency over the range considered. For this comparison RN is taken at a peak orifice particle velocity equal to the orifice average velocity at which RF is measured. The differential resistance RD is the small signal acoustic resistance measured with a superimposed unidirectional flow. RD has been found to be approximately equal 2RF.