The effects produced by the acoustic diffuse field excitations are considered next with reference to the spectra of the total kinetic energy PSD and total radiated sound power PSD shown in plots (c) and (d) of Figure 11. At frequencies below acoustic coincidence, the spectrum of the kinetic energy is similar to that found for the 45o acoustic plane wave excitation (thick-solid line in plot (a)). Thus, above the first resonance frequency of the plate, the spectrum of the kinetic energy tends to fall following the mass law with a 6 dB/octave slope. Also, the spectrum becomes increasingly smooth and characterised by wide band crests due to the overlapping of a linearly increasing number of modal responses. Around the critical frequency at about 7.54 kHz, the spectrum shows the wide frequency band ridge with multiple resonance peaks. However, this ridge is relatively modest in comparison to that found for the grazing acoustic plane wave excitation and extends over a wider frequency band. This is because, as schematically shown in Figure 9(b), the acoustic diffuse field excitation is composed by acoustic plane waves with a uniform distribution of angles of incidence. Thus the excitation coincidence phenomenon extends to all frequencies starting from the critical frequency (highlighted by the thick-dashed vertical line) to infinity. Since the energy of the diffuse excitation field is equally divided between waves at all angles of incidence, the excitation coincidence phenomenon at every frequency, and thus for every angle of incidence, is not as strong as that for the single plane wave with a fixed angle of incidence. However, it spans over a much wider frequency range, ideally up to infinity.
In general the observations made for the spectrum for the total kinetic energy also apply to the spectrum for the total radiated sound power. In fact, for frequencies below acoustic coincidence, the radiated sound power shown in plot (d) is similar to that found for the 45o acoustic plane wave excitation (solid line in plot b). Thus, at low frequencies, the spectrum of the radiated sound power PSD is characterised by a smaller number of well separated resonances since the sound radiation mechanism tends to filter out those resonances due to plate natural modes with both or one even mode orders. As the frequency rises above the fundamental resonance frequency of the plate, the spectrum of the mean radiated sound power tends to fall according to the mass law with a slope of 6 dB/octave. When the frequency reaches the critical frequency at about 7.54 kHz (highlighted by the thick-dashed vertical line), the spectrum shows a wide band ridge, which is less marked than that visible in plot (b) for the 45o acoustic plane wave excitation (thick-solid line) but is much more noticeable than that found in plot (c) for the kinetic energy due to the diffuse acoustic field excitation. This phenomenon is due to the fact that, on one hand, the diffuse acoustic field distributes the energy to plane waves with all angles of incidence and thus distributes the excitation coincidence effect over all frequencies above the critical frequency and, on the other hand, the sound radiation becomes very effective around the critical frequency.