The acoustical impedance of holes in the wall of flow ducts

The radiation impedance of circular and oblong holes in the wall of a flow duct has been measured as a function of the flow velocity. The boundary layer at the wall of the duct is thin compared to the dimensions of the orifices. At low Strouhal numbers (quasi-static case) and constant boundary layer thickness, the flow resistance of the orifice (real part of the impedance) increases in proportion to the flow velocity. The imaginary part of the impedance corresponds to a constant, negative attached mass above the orifice, i.e. the impedance is spring-like. In the transition range from air at rest to the quasi-static case (high Strouhal numbers) the impedance as a function of the flow velocity describes a spiral in the complex plane. The mechanism causing the flow dependence of the impedance is illustrated by a simple model of the flow above the orifice. As a practical example of the flow-dependent impedance of orifices, the flow-dependent sensitivity of a probe microphone used in flowing media is discussed.