Room Modes
Axial, tangential and oblique standing waves of a rectangular room, with pressure maps.
Room
| # | n x,y,z | f (Hz) | Type |
|---|---|---|---|
| 1 | 1, 0, 0 | 29.6 | axial |
| 2 | 0, 1, 0 | 40.8 | axial |
| 3 | 1, 1, 0 | 50.4 | tangential |
| 4 | 2, 0, 0 | 59.1 | axial |
| 5 | 0, 0, 1 | 66.0 | axial |
| 6 | 2, 1, 0 | 71.9 | tangential |
| 7 | 1, 0, 1 | 72.3 | tangential |
| 8 | 0, 1, 1 | 77.6 | tangential |
| 9 | 0, 2, 0 | 81.7 | axial |
| 10 | 1, 1, 1 | 83.0 | oblique |
| 11 | 1, 2, 0 | 86.9 | tangential |
| 12 | 2, 0, 1 | 88.6 | tangential |
| 13 | 3, 0, 0 | 88.7 | axial |
| 14 | 2, 1, 1 | 97.5 | oblique |
| 15 | 3, 1, 0 | 97.7 | tangential |
| 16 | 2, 2, 0 | 100.8 | tangential |
| 17 | 0, 2, 1 | 105.0 | tangential |
| 18 | 1, 2, 1 | 109.1 | oblique |
| 19 | 3, 0, 1 | 110.5 | tangential |
| 20 | 3, 1, 1 | 117.8 | oblique |
| 21 | 4, 0, 0 | 118.3 | axial |
| 22 | 2, 2, 1 | 120.5 | oblique |
| 23 | 3, 2, 0 | 120.6 | tangential |
| 24 | 0, 3, 0 | 122.5 | axial |
| 25 | 4, 1, 0 | 125.1 | tangential |
| 26 | 1, 3, 0 | 126.0 | tangential |
| 27 | 0, 0, 2 | 131.9 | axial |
| 28 | 1, 0, 2 | 135.2 | tangential |
| 29 | 4, 0, 1 | 135.4 | tangential |
| 30 | 2, 3, 0 | 136.0 | tangential |
| 31 | 3, 2, 1 | 137.4 | oblique |
| 32 | 0, 1, 2 | 138.1 | tangential |
| 33 | 0, 3, 1 | 139.1 | tangential |
| 34 | 1, 1, 2 | 141.2 | oblique |
| 35 | 4, 1, 1 | 141.4 | oblique |
| 36 | 1, 3, 1 | 142.2 | oblique |
| 37 | 4, 2, 0 | 143.7 | tangential |
| 38 | 2, 0, 2 | 144.6 | tangential |
| 39 | 5, 0, 0 | 147.8 | axial |
| 40 | 2, 1, 2 | 150.2 | oblique |
| 41 | 2, 3, 1 | 151.2 | oblique |
| 42 | 3, 3, 0 | 151.2 | tangential |
| 43 | 5, 1, 0 | 153.4 | tangential |
| 44 | 0, 2, 2 | 155.2 | tangential |
| 45 | 1, 2, 2 | 157.9 | oblique |
| 46 | 4, 2, 1 | 158.1 | oblique |
| 47 | 3, 0, 2 | 159.0 | tangential |
| 48 | 5, 0, 1 | 161.9 | tangential |
| 49 | 0, 4, 0 | 163.3 | axial |
| 50 | 3, 1, 2 | 164.1 | oblique |
| 51 | 3, 3, 1 | 165.0 | oblique |
| 52 | 1, 4, 0 | 166.0 | tangential |
| 53 | 2, 2, 2 | 166.0 | oblique |
| 54 | 5, 1, 1 | 167.0 | oblique |
| 55 | 5, 2, 0 | 168.9 | tangential |
| 56 | 4, 3, 0 | 170.3 | tangential |
| 57 | 2, 4, 0 | 173.7 | tangential |
| 58 | 0, 4, 1 | 176.1 | tangential |
| 59 | 4, 0, 2 | 177.2 | tangential |
| 60 | 6, 0, 0 | 177.4 | axial |
| 61 | 1, 4, 1 | 178.6 | oblique |
| 62 | 3, 2, 2 | 178.7 | oblique |
| 63 | 0, 3, 2 | 180.0 | tangential |
| 64 | 5, 2, 1 | 181.3 | oblique |
| 65 | 4, 1, 2 | 181.8 | oblique |
| 66 | 6, 1, 0 | 182.1 | tangential |
| 67 | 1, 3, 2 | 182.4 | oblique |
| 68 | 4, 3, 1 | 182.6 | oblique |
| 69 | 2, 4, 1 | 185.8 | oblique |
| 70 | 3, 4, 0 | 185.9 | tangential |
| 71 | 6, 0, 1 | 189.3 | tangential |
| 72 | 2, 3, 2 | 189.5 | oblique |
| 73 | 5, 3, 0 | 192.0 | tangential |
| 74 | 6, 1, 1 | 193.6 | oblique |
| 75 | 4, 2, 2 | 195.1 | oblique |
| 76 | 6, 2, 0 | 195.3 | tangential |
| 77 | 3, 4, 1 | 197.2 | oblique |
| 78 | 0, 0, 3 | 197.9 | axial |
| 79 | 5, 0, 2 | 198.1 | tangential |
Standing waves in a box
At low frequencies a room behaves as a resonator. Sound reflecting between parallel surfaces forms standing waves at discrete frequencies, the room modes or eigenfrequencies. For a rigid rectangular room:
- Axial modes (one non-zero index) involve two parallel surfaces and are the strongest.
- Tangential modes (two indices) involve four surfaces; about 3 dB weaker.
- Oblique modes (three indices) involve all six surfaces; about 6 dB weaker than axial modes.
Pressure distribution
The pressure of each mode varies as \cos(n_x\pi x/L)\cdot\cos(n_y\pi y/W)\cdot\cos(n_z\pi z/H). All modes have pressure maxima in the corners, which is why corner bass traps are effective and why a subwoofer in a corner excites every mode. The map shows the selected mode in plan at floor level; teal and amber are opposite phases, dark areas are nodes where that mode is inaudible.
Schroeder frequency
Above f_S modes overlap so densely that the field becomes statistically diffuse and the reverberation-time formulas apply. Below it, the response is dominated by individual modes, and treatment requires resonant absorbers or careful placement.
Good proportions
Rooms with dimensions that are equal or simple multiples (e.g. a cube, or 3×6×3 m) stack modes on the same frequency, producing strong peaks and gaps. Ratios such as 1 : 1.4 : 1.9 (Sepmeyer) or 1 : 1.28 : 1.54 (Louden) spread the modes more evenly.