Single Subwoofer Placement and Boundary Effect
Imagine, as shown in Fig. 21, at one end of your listening room, located on the center axis of the room and 1 meter out from the wall directly behind it, sits your subwoofer. At the opposite end of the room sits you, on the same central axis of the room and seated a meter away from the wall immediately behind you.
Further imagine, for the sake of discussion, your subwoofer has an on-axis amplitude response that measure perfectly flat, anechoically. Now let's fire up the subwoofer.
Once the subwoofer's energized, the first sound that reaches your ears is the direct sound, with the systems dead-flat frequency response intact and unaltered by the room's acoustic signature.
At the same time, sound is, of course, traveling in all directions, including those areas where the room modes are formed. Reaching those areas, it then excites the mode or modes, which store the energy, then release it, after a delay. That energy then continues its transit of the room's enclosed volume, eventually reaching your ears, delayed behind the first-arrival sound, and with amplitude altered. If the resonance decays at a rate such that the primary sound event ends before the resonance decays to a sub-audible level, than the LF portion of the audible spectrum begins to sound, subjectively speaking, "loose" or "poorly defined".
The net effect is that you now perceive the subwoofer's response through the "lens", as it were, of the room's acoustic signature and the perceived frequency response now features all the evidence of the room's resonances: peaks & dips that in some circumstances can reach 10s of dBs in magnitude.
Of the three types of modes (axial, tangential & oblique) that can set up within a listening space, it's the axial modes (e.g.: Figs., 1 & 2) that will have the most noticeable effect on perceived system response at the listening position. The degree to which any of these discrete, LF modes, affect the perceived response depends largely upon the location of the listening position and the location of the subs within the listening space.
These room modes don't require a special type of signal set up: sine wave, pink noise, music or a hand clap: so long as energy is applied at the correct, required frequencies the mode will be excited. It does not require a steady tone. On the other hand, if the acoustic energy applied to the listening room's space is at a frequency where no mode exists, no resonance sets up, thus no effect on the perceived response at the listening position; there's no frequency-specific modal energy build up in the space.
Room resonances truly are resonant systems: they have a specific Q ( the ratio of energy stored by the reactive components of the resonance - mass and compliance - to the energy dissipated (absorption, etc), bandwidth & characteristic natural frequency. Their amplitude depends upon the excitation period and their duration depends upon the absorptive qualities of the walls, floor & ceiling and the volume of air enclosed by the boundaries.
Along with room resonances, the effects of the room's boundaries play a key role in determining the subwoofer system's response as perceived at the listening position.
For this portion of the analysis I ran a series of simulations using a vented subwoofer, sporting a single 12" driver, with an amplitude response characterized by -3dB points at ~14Hz and ~80 Hz. For reference I'll start by modeling the system in both 4π steradian (full space) and 2π steradian (half-space) domains. We'll be using the 2π steradian system response as our reference measurement.
With the front panel of the subwoofer modeled flush with the radiation boundary (which illustrates the half-space model) and the source of acoustic energy being small compared with the wavelengths being radiated (not forgetting the low pass -3dB point is set at 80 Hz), the effects of diffraction & increasing directivity will not be seen in the response. As expected, it behaves like an omnidirectional radiator bolted in to a wall of infinite linear dimensions.
Having established a 2π steradian (half-space) response of the system as a reference point (as seen in Fig. 22) we can now exam the effect of boundaries on system response.
In Figure 23 we see the cabinet positioned such that its back panel is flush against a wall. No other boundary effects are presented in the simulation. The simulation is then re-run, this time with the cabinet moved 1m away from the wall. The "r" value is the distance from the system reference point (the center of the faceplate) to the boundary located immediately behind it. .683m is also the depth of the system's cabinet, therefore when r = .683m, the back of the cabinet is situated flush against the boundary immediately behind it. Please note that in these simulations, as the cabinet's position is changed, the listening position of the microphone changes accordingly, thus maintaining the 1m, on axis orientation of the mic.
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