spatial pattern (same circumferential, longitudinal order or their
combinations). In addition, the velocity continuity relation on
MPP surface causes the equal modal amplitudes of these dominating
modes. Hence, at this frequency, the sound pressures on the
two sides of the MPP are equal and in phase everywhere over the
MPP surface. Recalling its working mechanism, a MPP dissipates
acoustic energy through the oscillation of air inside its holes, as a
result of the pressure difference between the two sides of MPP. If
the sound pressures on the two sides of MPP are equal and in
phase, the air inside holes cannot vibrate and hence no energy
dissipation could possibly occur. Therefore, at this frequency,
MPP behaves like a rigid wall to the main sound field and the resultant
sound pressure level is the same as it is in the rigid-walled
case. Similar phenomenon can also be observed at 1536 Hz in
Fig. 4(c), at which the sound pressure field is dominated by the
longitudinal rigid-walled mode. Remember that the undamped
resonances happen at resonant frequencies of the non-radial
modes only. If the order of the radial mode is non-zero, MPP will
be activated and serves as an absorbing boundary. Fig. 4(b) and
(d) present the sound pressure distributions at 1046 Hz and
1514 Hz, corresponding to the (0, 1,0) and (1, 1,1) mode, respectively,
in the absence of the MPP. After installing the MPP,
apparently, the wave patterns on each side of the MPP are
different, resulting in a sound pressure change across the MPP
and consequently a significantly reduced sound pressure level
inside the cavity as shown in Fig. 2. It is relevant to note that
Fig. 4(b) and (d) show no modal sound pressure distribution, as
evidenced by the loss of symmetry in the circumferential
(Fig. 4(c)) or longitudinal (Fig. 4(d)) directions. This is also an indication
that MPP takes effects and modifies the original modes
(before MPP is installed) by coupling the two acoustic media.
Since the point source is arbitrarily placed inside the main cavity,
the sound distributions shown in Fig. 4(b) and (d) are no longer
single-mode dominant and symmetrical.