Developments in Ceramic Materials Research

158
ω = c
0
Dimitris Skarlatos, Tilemachos Zakinthinos and Ioanis Koumanoudis
s
( d + d ) V
cor res
dcor is the “end correction” of the aperture neck. For a resonator with aperture radius r the
end correction can be approximated by:
16r
dcor = ≈ 1.7r
3π
Resonance in quarter wavelength resonators is set up when the cavity length corresponds
to a quarter wavelength (or odd multiple) of the frequency of interest. The fundamental
frequency of a quarter wavelength resonators is [42].
2π
c
ω 0 =
4l
More accurate formulas for resonators with specific geometries have been proposed by
Alster, Mohring, Tang and other researchers [43, 44, 45].
Helmholtz resonators have additional resonant frequencies higher than that given by
equation (1). The origin of these higher frequencies is quite different from that of the
fundamental, for they result from standing waves in the cavity, rather from the oscillatory
motion of the mass of the fluid in the neck. The overtone frequencies therefore, depend on the
shape of the cavity and are not harmonically related to the fundamental. In general, the
frequency of the first overtone is several times as great as that of the fundamental [46].
The sharpness of resonance of a driven Helmholtz resonator, measured by its quality
factor is given by:
Q
res
=
V ( d + d
s
)
res cor
2π 3
3
when a resonator is a member of a group of resonators in a wall its function will be affected
by the interaction from the other resonators. If the resonators are placed in the wall
sufficiently far apart, they should act independently of each other. The limiting distance is
[41]:
d
0
=
λ0
2π
The principal function of resonators is sound absorption. The absorbing power of a
resonator is characterized by the absorption cross section σ abs which is defined as the ratio of
sound energy being absorbed per second by it and the intensity which the incident sound
(1)
(2)
(3)
(4)
(5)