Handbook for Sound Engineers

130 Chapter 6

of standard building materials. Our next test room is
16 ft long by 12 ft wide with a ceiling height of 8 ft
(4.88 m × 3.66 m × 2.44 m). Table 6-4 shows the length,
width, and height modes, and Table 6-5 shows the same
data sorted into order according to frequency.

• If we examine the data in Fig. 6-6 we see that there
  are some frequencies which are supported by only
  one dimension. 35 Hz, for example, is only supported
  by the 16 ft (4.88 m) dimension. Other frequencies,
  like 70 Hz, occur twice and are supported by length
  and height. Still others like 141 Hz occur three times
  and are supported by all three dimensions. In the
  nomograph of Fig. 6-6, the height of the line indi-
  cates the magnitude of the mode. This room is clearly

better than a cube, but it is far from ideal as there are

many frequencies which will stand out. 70 Hz,

141 Hz, 211 Hz, 282 Hz, and 253 Hz are all going to

be problem frequencies in this room.

Now consider a room that has dimensions that might

be well suited for an audio room; 23 ft long by 17 ft

wide by 9 ft high ceiling (7 m × 5.18 m × 2.74 m). The

sorted data and nomograph are shown in Table 6-6 and

Fig. 6-7.

The data in Fig. 6-7 look quite different from the

data in Fig. 6-5 and Fig. 6-6. There are no instances

where all three dimensions support the same frequency.

There is also a reasonably good distribution of modes

across the spectrum. There are a few places where the

difference between the modes is quite small, like the

space between the 4,0,0 and the 0,3,0. These three

rooms, the cube, the room with dimensions determined

by the builder, and the last room demonstrate the first

important principle when dealing with room modes.

Table 6-4. Room Modes of a Rectangular Room
16 Ft × 12 Ft × 8 Ft

Length Modes Width Mode Height Modes

35.31 1,0,0 47.08 0,1,0 70.63 0,0,1

70.63 2,0,0 94.17 0,2,0 141.25 0,0,2

105.94 3,0,0 141.25 0,3,0 211.88 0,0,3

141.25 4,0,0 188.33 0,4,0 282.50 0,0,4

176.56 5,0,0 235.42 0,5,0 353.13 0,0,5

211.88 6,0,0 282.50 0,6,0 423.75 0,0,6

247.19 7,0,0 329.58 0,7,0 494.38 0,0,7

282.50 8,0,0 376.67 0,8,0 565.00 0,0,8

317.81 9,0,0 423.75 0,9,0 635.63 0,0,9

353.13 10,0,0 470.83 0,10,0 706.25 0,0,10

Table 6-5. Modes of a 16 Ft × 12 Ft × 8 Ft Room
Sorted by Frequency

Frequency Modes Spacing Frequency Modes Spacing

35.31 1,0,0 282.50 8,0,0 35.31

47.08 0,1,0 11.77 282.50 0,6,0 0.00

70.63 2,0,0 23.54 282.50 0,0,4 0.00

70.63 0,0,1 0.00 317.81 9,0,0 35.31

94.17 0,2,0 23.54 329.58 0,7,0 11.77

105.94 3,0,0 11.77 353.13 10,0,0 23.54

141.25 4,0,0 35.31 353.13 0,0,5 0.00

141.25 0,3,0 0.00 376.67 0,8,0 23.54

141.25 0,0,2 0.00 423.75 0,9,0 47.08

176.56 5,0,0 35.31 423.75 0,0,6 0.00

188.33 0,4,0 11.77 470.83 0,10,0 47.08

211.88 6,0,0 23.54 494.38 0,0,7 23.54

211.88 0,0,3 0.00 565.00 0,0,8 70.63

235.42 0,5,0 23.54 635.63 0,0,9 70.63

247.19 7,0,0 11.77 706.25 0,0,10 70.63

Figure 6-6. Number of modes and frequencies for a room

16ft×12ft×8ft. From AcousticX.

Table 6-6. Data for a Room 23 Ft × 17 Ft × 9 Ft

Frequency Modes Spacing Frequency Modes Spacing

24.57 1,0,0 196.52 8,0,0 8.19

33.24 0,1,0 8.67 199.41 0,6,0 2.89

49.13 2,0,0 15.90 221.09 9,0,0 21.68

62.78 0,0,1 13.65 232.65 0,7,0 11.56

66.47 0,2,0 3.69 245.65 10,0,0 13.01

73.70 3,0,0 7.23 251.11 0,0,4 5.46

98.26 4,0,0 24.57 265.88 0,8,0 14.77

99.71 0,3,0 1.45 299.12 0,9,0 33.24

122.83 5,0,0 23.12 313.89 0,0,5 14.77

125.56 0,0,2 2.73 332.35 0,10,0 18.46

132.94 0,4,0 7.39 376.67 0,0,6 44.31

147.39 6,0,0 14.45 439.44 0,0,7 62.78

166.18 0,5,0 18.79 502.22 0,0,8 62.78

171.96 7,0,0 5.78 565.00 0,0,9 62.78

188.33 0,0,3 16.38 627.78 0,0,10 62.78