In 1896 Rayleigh showed that the air enclosed in a room has an infinite number of normal modes of vibration. These are referred to as room modes or standing waves. The frequencies at which these modes occur are given by the following:
f = c/2 (sqRt (p/L)2 + (q/W)2 + (r/H)2)
c is the speed of sound
L is the length of the room
W is the width of the room
H is the height of the room
And p, q, and r are the integers 0, 1, 2, 3.
As we can see from the formula, speaker placement has no bearing on the matter. The standing wave condition is set up only when the air particle velocity at the boundary is zero. Whenever air particle velocity is zero, pressure is at the maximum level. (If the walls are not perfect reflectors, losses at the walls will affect the heights of the maxima and depths of the minima.)
All room modes are represented as a sinusoidal wave form and for any given modal frequency the peak is always located at the room boundary. Thus, the location of any null or peak will be a function of the boundary and frequency and not a function of speaker placement. Since the condition for a standing wave is that particle velocity must be zero at each opposite reflecting surface, the peak of the wave must occur at the wall surface, and, hence, standing waves can only occur where the distance between the boundaries are an exact multiple of the wave length. By extension, then nulls are a function of only the distance between the boundaries and the frequency (wave length). While speaker placement will not affect the location of peaks and nulls, it will affect the maxima and minima of the effect.
In the same manner, you cannot have an asymetrical standing wave form. For example, in an 18' room, you cannot have a null at 6' without also a null at 12'. Moving the speaker from the front to the back of the room will simply alter the location of the speaker, not the location of peaks and nulls. Moving the speaker out away from the boundaries, by various distances, will also not affect the existence, or location of, nulls and peaks ... it will affect the maxima and minma of certain (not all) modes.
However, as I have previously suggested, we ought be more concerned with the minima and maxima of a standing wave rather than on the placement of the peaks and nulls (why fix a problem you donâ€™t have?) Modal Potency, Modal Frequency Density, and Modal Bandwidth are more important criteria in establishing the playback venue. Unfortunately, youâ€™re not going to effectively model the maxima and minima from a free spreadsheet program.
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