End-correction factor (thin plate)

The extra mass length of a hole in the thin-plate physics baseline, as a multiple of its diameter: the air set in motion just outside the two ends of the hole, which adds to the inertia of the air inside it.

Last updated 2026-11-03

Theory

The air in a hole moves together with some air beside each opening. Its inertia is that of a slug longer than the plate by the end correction $\epsilon d$ (both sides together). For an isolated circular hole in a thin baffle the classical value is $\epsilon = 0.85$ (Rayleigh's piston result, as quoted by (Sullivan and Crocker, 1978) and (Kirby and Cummings, 1998)). The baseline adds it as a reactance, equation (1), multiplied by the hole-interaction factor when Hole interaction (thin plate) is set.

The other models have their own fixed end corrections:

$0.75\,d$ (Sullivan & Crocker, cross-flow);
$0.85\,d\,\delta/\delta_0$ (Kirby & Cummings);
$0.5\,d f_{int}$ (Elnady).

Equations

\zeta_{end} = \frac{i\omega\rho\,\epsilon\,f\,d}{\rho c} = ik\,\epsilon f d

(1)

where	meaning	unit
$\epsilon$	End-correction factor (this field)	-
$f$	Hole-interaction factor (1 for none)	-
$d$	Hole diameter	m
$k$	Wavenumber	1/m

Default and rule

Default: 0.85 (Rayleigh)
Rule: 0.85.
Source: The value 0.85 d is Rayleigh's end correction (Rayleigh, 1945), as quoted by (Sullivan and Crocker, 1978) and (Kirby and Cummings, 1998).

Valid range 0 < ε ≤ 2 (thin-plate physics baseline only)

Values

Above 0, at most 2. A larger value lowers the resonance frequencies of resonators behind the perforate.

Applies to

The thin-plate physics baseline only.

Theory

Equations

Default and rule

Valid range 0 < ε ≤ 2 (thin-plate physics baseline only)

Related 5

References 3