Oscillations, Waves, and Interactions - GWDG

Sound absorption, sound amplification, and flow control in ducts 77
peak frequency [kHz] peak amplitude [dB]
50
40
30
20
10
1
0
1.6
1.4
1.2
gap width = 5 mm
10
6 cavities
8
5 mm 10 12.5
10
13 16
0.15 0.2 0.25 0.3 0.35
(flow velocity) / (speed of sound)
6
8
13
10 cavities
Figure 3. Amplitude and mid-frequency of the A 1 -peak of Fig. 2(b) as functions of the flow
velocity. The number of cavities has been varied while the full cross-section of the pipe was
open to the flow (blue and black solid curves, denoted by the number of cavities), and the
cross-section of the duct was reduced by insertion of a coaxial cylindrical body while the
number of cavities (16) remained constant (red dashed curves, denoted by the gap width
between the central body and the duct wall).
with a low resonance frequency (840 Hz) corresponding to the dimensions of the
cavities that are shown in Fig. 1. The lowest cut-on frequency of higher-order modes
in the rigid pipes upstream and downstream of the resonator section is 4 kHz. So
for frequencies in the order of the resonance frequency all higher-order modes are
evanescent and only the fundamental axisymmetric mode can propagate.
We first became aware of the sound amplification by some faint narrow-band whispering
superimposed on the flow noise in the laboratory. The pressure spectra (Fig. 2)
measured far upstream and far downstream of the resonator section reveal that this
sound originates in the resonator section and is radiated mainly in the direction of
the flow. The sample spectrum in Fig. 2(a) shows a few prominent peaks on top of
an otherwise rather constant power spectral density, and the development of these
peaks with increasing flow velocity † U is depicted in Figs. 2(b) and (c) where the
† Although the compressibility of the air is not essential for the considered phenomena,
the average of the flow velocity over the cross-sectional area of the pipe U is normalized to
12.5
16