Developments in Ceramic Materials Research

160
Dimitris Skarlatos, Tilemachos Zakinthinos and Ioanis Koumanoudis
In this equation η is the viscosity and ρ the density of air.
The normalized radiation resistance for a resonator in an infinite wall is [41, 47, 48].
2π
s
θr
= 2
λ
A combination of equations (8), (9) and (10) gives for μ
2
dλ
μ = 2ρηω
2πρcrs
At resonance the absorption cross section reaches its maximum value. The maximum
value under optimum conditions is
σ
abs,max
2
λ0
=
2π
The energy storage in the resonator affects the acoustics of the room. We can assume
instantaneous energy exchange between the room and the resonator, a condition which
Rschevkin showed to be satisfied in all practical cases [47]. The moving air in the neck
radiates sound into the surrounding medium in the same manner as an open ended pipe. Thus
the resonator behaves like a circular piston sitting on a very large baffle. The radiation pattern
of such a source is omni directional. However it must be noted that when the resonator is
embedded in a wall the radiation of sound from the aperture is restricted to the half space only
and the corresponding energy density is greater by a factor 2. When the resonator is
embedded in a corner the value of this factor is 4.
The intensity of the radiated power from a resonator in a wall at a distance x in the
matched case ( μ = 1)
at resonance is given by the equation [48]:
⎛ λ ⎞
Is = ⎜ ⎟ I
⎝2πx⎠ 2
0
where λ is the wavelength and I0 the intensity of the incident sound.
The scattering of sound by a resonator is probably more important than its absorption.
The power scattered by a resonator and the corresponding cross section is given by [47]:
2 2
λ g 4
Dc
w = Dc=
σ
r 2 2
res
2 π (1 ) 4
2 ⎡ 1 ⎤ + μ
1+
Qres g−
⎢
g
⎥
⎣ ⎦
(11)
(12)
(13)
(14)