Characterizing holes in duct walls using resonance frequencies

The current paper demonstrates that the technique recently used by de Salis and Oldham for the sizing and location of blockages in ducts using resonance and antiresonance value shifts [J. Sound Vib. 221(1), 180-186 (1999)] may be successfully applied to the detection, location, and sizing of small holes in duct walls. It is shown that when the blockage area function reconstruction process is applied using resonance and antiresonance frequencies determined from a single measurement of sound pressure within a duct, the position of a hole in the duct wall is revealed as the beginning of an apparent gradual expansion. This expansion is termed the effective expansion function and emanates from an initial positive dc shift. Once the hole has been located, a simple impedance model of the duct incorporating the hole location and the measured wave number at the first-order duct resonance may be derived which allows the determination of the radius of the side hole from a simple quadratic equation. This hole-sizing technique is also successfully applied to thin slits in duct walls using an equivalent radius approach, and is shown to be highly accurate for slit-shaped holes with cross-sectional length to width aspect ratios of up to 28:1.