The acoustic response of a circular hole with mean flow passing through it is highly relevant to Helmholtz resonators,
fuel injectors, perforated plates, screens, liners and many other engineering applications. A widely used analytical
model [M. S. Howe. On the theory of unsteady high Reynolds number flow through a circular aperture, Proc. of
the Royal Soc. A. 366, 1725 (1979), 205223] which assumes an infinitesimally short hole was recently shown to
be insufficient for predicting the impedance of holes with a finite length. In the present work, an analytical model
based on the Green’s function method is developed to take the hole length into consideration for “short” holes. The
importance of capturing the modified vortex noise accurately is shown. The vortices shed at the hole inlet edge are
convected to the hole outlet and further downstream to form a vortex sheet. This couples with the acoustic waves
and this coupling has the potential to generate as well as absorb acoustic energy in the low frequency region. The
impedance predicted by this model shows the importance of capturing the path of the shed vortex. When the vortex
path is captured accurately, the impedance predictions agree well with previous experimental and CFD results, for
example predicting the potential for generation of acoustic energy at higher frequencies. For “long” holes, a simplified
model which combines Howe’s model with plane acoustic waves within the hole is developed. It is shown that the
most important effect in this case is the acoustic non-compactness of the hole.