Oscillations, Waves, and Interactions - GWDG

(pressure drop) / (dynamic pressure)
0.32
0.3
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
Sound absorption, sound amplification, and flow control in ducts 83
(a)
0.12
0.12 0.14 0.16 0.18 0.2 0.22 0.24
(b)
0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28
argument of function DP in Eq. (1)
Figure 9. Relation between the pressure drop and the pressure amplitude at the rear end
of the resonator section according to Eq. (1). (a) m = 0; pac = transmitted sound pressure
amplitude; U/c = 0.2 (thin curves), frequencies: 907 Hz (black, dash-dotted), 1007 Hz (red,
solid), 1087 Hz (green, dashed); U/c = 0.25 (thick curves), frequencies: 1007 Hz (black,
dash-dotted), 1087 Hz (red, solid), 1127 Hz (green, dashed). (b) m = 1, pac = pressure
amplitude in the backmost cavity; U/c = 0.2 (thin curves), frequencies: 1207 Hz (red,
solid), 1307 Hz (green, dashed); U/c = 0.25 (thick curve), frequency: 1207 Hz (red, solid).
(iv) The pressure drop ∆p along the lined duct section and the amplitude pac of the
transmitted sound wave are related by
�� �2 � �2
∆p
ptb κ(f, U) · pac
= DP (U) +
pdyn pdyn
pdyn
�
, (1)
wherein pdyn is the dynamic pressure. The quantities ptb(U) and κ(f, U) are fitted
to the experimental data except for a free common factor which is adapted such
that DP{· · ·} becomes the identity function for small sound pressure amplitudes;
κ(f, U) increases with increasing frequency and with decreasing flow velocity. As
seen from Fig. 9(a), DP{· · ·} does not differ very much from the identity function
also at large sound amplitudes. However, only a few experimental data were suited
for this evaluation, so the universality of DP{· · ·} may be questioned. In fact, when
higher-order mode sound irradiation (see next Section) is applied to the resonator
section, strongly nonlinear and all but universal relations are found between ∆p and
p 2 ac. Fig. 9(b) shows several examples where pac is the pressure amplitude in the
backmost cavity of the resonator section.