Small Room Acoustics 129axial modes (for now) we see a fundamental mode at
565/12 or 47.08 Hz. If we continue the series, looking at
the 1,0,0; 2,0,0; 3,0,0...10,0,0 modes we see the results
in Table 6-1.
Before we continue the calculation, let us examine
what this table is indicating. The frequencies listed are
those and only those that are supported by these two
walls; that is to say there will be some resonance at
these frequencies but at no others. When the source is
cut off, the energy stored in a mode decays logarithmi-
cally. The actual rate of decay is determined by the type
of mode and the absorptive characteristics of whatever
surfaces are involved with that mode. An observer in
this situation, making a sound with frequency content
that includes 141 Hz, may hear a slight increase in
amplitude depending on the location in the room. The
observer will also hear a slightly longer decay at
141 Hz. At 155 Hz, for example, there will be no
support or resonance anywhere between these two
surfaces. The decay will be virtually instantaneous as
there is no resonant system to store the energy. Of
course, in a cube the modes supported by the other
dimensions (0,1,0; 0,2,0; 0,3,0 ... 0,10,0 and 0,0,1;
0,0,2; 0,0,3... 0,0,10) will all be identical, Table 6-2.
In the cube, all three sets of surfaces are supporting
the same frequencies and no others. Talking in such a
room is like singing in the shower. The shower stall
supports some frequencies, but not others. You tend to
sing at those frequencies because the longer decay at
those frequencies adds a sense of fullness to the sound.
Table 6-2 can be made more useful by listing all the
modes in order to better examine the relationship
between them. Table 6-3 is such a listing. In this table,
we have included the spacing in Hz between a mode
and the one previous to it.We can clearly see the triple modes that occur at
every axial modal frequency, and there is 47 Hz (equal
to f 0 ) between each cluster. The space between each
cluster is important because if a cluster of modes or even
a single mode is separated by more than about 20 Hz
from it nearest neighbor, it will be quite audible as there
is no masking from nearby modes. Consider another
room that does not have a good set of dimensions for a
sound room, but represents a typical room size becauseTable 6-1. Modal Frequencies for a 12 Ft Cube
Room (Axial Only)
Length Modes Length Modes47.08 1,0,0 282.50 6,0,0
94.17 2,0,0 329.58 7,0,0
141.25 3,0,0 376.67 8,0,0
188.33 4,0,0 423.75 9,0,0
235.42 5,0,0 470.83 10,0,0Table 6-2. Axial Modes in a Cube Supported in Each
Dimension
Length Modes Width Modes Height Modes47.08 1,0,0 47.08 0,1,0 47.08 0,0,1
94.17 2,0,0 94.17 0,2,0 94.17 0,0,2
141.25 3,0,0 141.25 0,3,0 141.25 0,0,3
188.33 4,0,0 188.33 0,4,0 188.33 0,0,4
235.42 5,0,0 235.42 0,5,0 235.42 0,0,5
282.50 6,0,0 282.50 0,6,0 282.50 0,0,6
329.58 7,0,0 329.58 0,7,0 329.58 0,0,7
376.67 8,0,0 376.67 0,8,0 376.67 0,0,8
423.75 9,0,0 423.75 0,9,0 423.75 0,0,9
470.83 10,0,0 470.83 0,10,0 470.83 0,0,10Table 6-3. All of the Axial Modes of the Cube in
Table 6-1 and Table 6-2
Frequency Modes Spacing Frequency Modes Spacing47.08 1,0,0 282.50 6,0,0 47.08
47.08 0,1,0 0.00 282.50 0,6,0 0.00
47.08 0,0,1 0.00 282.50 0,0,6 0.00
94.17 2,0,0 47.08 329.58 7,0,0 47.08
94.17 0,2,0 0.00 329.58 0,7,0 0.00
94.17 0,0,2 0.00 329.58 0,0,7 0.00
141.25 3,0,0 47.08 376.67 8,0,0 47.08
141.25 0,3,0 0.00 376.67 0,8,0 0.00
141.25 0,0,3 0.00 376.67 0,0,8 0.00
188.33 4,0,0 47.08 423.75 9,0,0 47.08
188.33 0,4,0 0.00 423.75 0,9,0 0.00
188.33 0,0,4 0.00 423.75 0,0,9 0.00
235.42 5,0,0 47.08 470.83 10,0,0 47.08
235.42 0,5,0 0.00 470.83 0,10,0 0.00
235.42 0,0,5 0.00 470.83 0,0,10 0.00Figure 6-5. Number of axial modes and frequencies for a
cube room. From AcousticX.