Theory

The acoustic flow in a narrow slit is a viscous oscillating flow between two parallel walls. The ratio of the slit width to the viscous boundary-layer thickness, the shear wave number $k_s$ , decides the behaviour: at small $k_s$ the flow is dominated by viscosity (a frequency-independent resistance), at large $k_s$ by inertia (a mass reactance) Kabral et al. (2014). The end correction of slits is negligible Kabral (2015), so the reactance is the inner part alone.

The steady flow through the slits, used by the flow solution of the same wall, is the limit of the same expression at zero frequency: a Poiseuille resistance $12\mu t/(\sigma b^2)$ per unit face velocity.

Equations

k_s = b\,\sqrt{\frac{\omega}{4\nu}}

(1)

where	meaning	unit
$k_s$	Shear wave number of the slit	-
$b$	Slit width	m
$\omega$	Angular frequency	rad/s
$\nu$	Kinematic viscosity at the operating state	m²/s

z_{s,i} = \frac{i\omega t}{\sigma c}\left[1 - \frac{\tanh(k_s\sqrt{i})}{k_s\sqrt{i}}\right]^{-1}

(2)

where	meaning	unit
$z_{s,i}$	Normalised inner impedance of the slit plate	-
$t$	Plate thickness	m
$\sigma$	Open-area ratio	-

Default and rule

Default: 0.2 mm
Rule: 0.2 mm (a typical value; enter the panel's slit width).
Source: Kabral et al. (2014), eqs. 2-4, from Guo et al. (2008).

Valid range 0.05 - 1 mm (micro-perforate)

Size

Outside 0.05 - 1 mm the plate is not a micro-perforate; the acoustic QA lists it.

Theory

Equations

Default and rule

Valid range 0.05 - 1 mm (micro-perforate)

Related 4

References 3