Acoustics - Consideration on resonance modes within a closed environment

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We have established that the distance between the walls influences the frequencies of the modes that are excited. The arising of modes is a phenomenon that must be kept under strict control, because they risk heavily tampering the frequency content of a sound within an enclosed environment. The ideal situation is when an environment has a flat response; this means that it reproduces each frequency with the same amplitude with which it had been generated in the first place. Let's suppose we are working in a room that generates a resonance mode along its length with a frequency of 800 Hz. Each time we play a sound in the room, the 800 Hz frequency will be reinforced by the mode and therefore our perception of 800 Hz will be eschewed. If the room's width is also such as to generate a mode with a resonance frequency of 800 Hz, the two mode's influence shall be greater. If, in addition to the former two dimensions, the height of the room also generates the same mode, we will have a sound in which the 800 Hz dominates over all other frequencies. Clearly this situation is harmful from the point of view of sound: the 800 Hz frequency value is overly emphasized compared to the other frequencies being reproduced within the room. In this case the room's response is far from being flat, but rather, has an evident peak at the 800 Hz frequency. Fortunately the situation we have just described, namely a cube-shaped room, is a worst case scenario. If we were to have a room where the three dimensions are different to one another, the three primary axial modes would also be different to one another and distributed on three separate frequencies. Though undoubtedly better than the previous cube-shaped room, this situation still creates strong unevenness between the three resonance frequencies (and on their multiples, since we can't always ignore the influence of the higher modes on the primary mode). Acoustics studies, in particular those focusing on mode-distribution, have led to suggestions regarding the ratios between the three dimensions in a room on how to get a relatively uniform distribution over the entire audible spectrum. The following are some of the mentioned ratios:

Table 15.1. Room dimension ratios 

d1d2/d1d3/d1
11.141.39
11.281.54
11.62.33

where d1, d2 and d3 identify the three dimensions of a room, namely: height, length, and width. These values can be applied in any order to the dimensions of an environment, so long as the ratio between the values is preserved. It must be highlighted that these triads are merely suggestions based on mathematical speculations, not universally applicable laws. In order to have a truly uniform distribution of modes in a room, you'd need to design environments with non-parallel walls. This way the distance between two walls in front of each other varies continually and therefore the modes that are generated are distributed more or less equally over an entire frequency-range. Generally speaking the greatest problems with modes are encountered at low frequencies. This happens because low frequency modes aggregate in certain frequency zones whilst high frequency modes are distributed equally over the frequency spectrum.








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