14 × 14 × 9 ft room
Every standing wave this room supports below 300 Hz, solved from its geometry alone. Lowest mode 40.2 Hz on the length; 18 axial, 81 tangential and 97 oblique modes in total.
Mode distribution to 300 Hz
Every mode this room supports, at its exact frequency. Even spacing reads as a well-behaved room; a wide gap followed by a clump is where it will sound hollow and then boom.
Volume
50.0 m³
1764 ft³, 83.2 m² of surface
Worst axial gap
40.2 Hz
widest hole between adjacent axial modes under 200 Hz
Densest cluster
7 modes at 179 Hz
modes within 5 Hz of each other, below 200 Hz
Bolt criterion
outside
ratio 1 : 1.56 : 1.56 (height : width : length)
The three fundamentals
One per pair of parallel surfaces, at c/2L with c = 343 m/s. These are the loudest and most audible resonances in the room; everything else is built on them.
length
40.2Hz
14 ft · half-wavelength fit
width
40.2Hz
14 ft · half-wavelength fit
height
62.5Hz
9 ft · half-wavelength fit
Axial modes in full18 modes
The modes that run between one pair of parallel surfaces. They carry the most energy and are the ones worth treating first.
| Frequency | Axis | Order | Indices (nx, ny, nz) |
|---|---|---|---|
| 40.2 Hz | width | 1 | 0, 1, 0 |
| 40.2 Hz | length | 1 | 1, 0, 0 |
| 62.5 Hz | height | 1 | 0, 0, 1 |
| 80.4 Hz | width | 2 | 0, 2, 0 |
| 80.4 Hz | length | 2 | 2, 0, 0 |
| 120.6 Hz | width | 3 | 0, 3, 0 |
| 120.6 Hz | length | 3 | 3, 0, 0 |
| 125.0 Hz | height | 2 | 0, 0, 2 |
| 160.8 Hz | width | 4 | 0, 4, 0 |
| 160.8 Hz | length | 4 | 4, 0, 0 |
| 187.6 Hz | height | 3 | 0, 0, 3 |
| 201.0 Hz | width | 5 | 0, 5, 0 |
| 201.0 Hz | length | 5 | 5, 0, 0 |
| 241.1 Hz | width | 6 | 0, 6, 0 |
| 241.1 Hz | length | 6 | 6, 0, 0 |
| 250.1 Hz | height | 4 | 0, 0, 4 |
| 281.3 Hz | width | 7 | 0, 7, 0 |
| 281.3 Hz | length | 7 | 7, 0, 0 |
Questions this room answers
What is the lowest room mode in a 14 × 14 × 9 ft room?
40.2 Hz, set by the length (14 ft) dimension. A half-wavelength has to fit between the two parallel surfaces, so the first mode is c/2L — with c = 343 m/s at 20 °C. Below this frequency the room cannot support a resonance at all, and bass output falls off regardless of the loudspeaker.
Where will a 14 × 14 × 9 ft room sound uneven?
The densest clustering below 200 Hz is 7 modes within 5 Hz of each other around 179 Hz — expect that region to sound louder and to ring longer. The largest gap between adjacent axial modes below 200 Hz is 40.2 Hz, and wide gaps are heard as a hole, not as neutrality.
Are 14 × 14 × 9 ft proportions good for a listening or control room?
The ratio (1 : 1.56 : 1.56, height : width : length) falls outside the Bolt area, the region Bolt published in 1946 for comparatively even low-frequency mode distribution. In practice that means modes bunch in some places and leave gaps elsewhere — treatable, but it is working against the geometry rather than with it.
Above what frequency do modes stop mattering here?
The Schroeder frequency for this 50.0 m³ volume is 155 Hz if RT60 is 0.3 s, and 219 Hz if RT60 is 0.6 s. Above it the modes overlap densely enough to behave statistically rather than individually. RT60 is a property of the materials in the room, not of its shape, so this page can only bracket it — measure your own to place the crossover exactly.
One dimension different
The comparison worth making before you build: change one dimension by a foot and every mode moves.
Method and limits. Frequencies solve f = (c/2)·√((nx/Lx)² + (ny/Ly)² + (nz/Lz)²) for a rectangular room with rigid boundaries, at c = 343 m/s (20 °C). Real rooms have windows, doors, soffits and non-rigid walls, all of which shift and damp these frequencies — treat this as where to look, not as a measurement. The Schroeder crossover additionally depends on RT60, which is a property of the room's materials and not of its shape, so it is quoted here against two assumed values rather than as a fact about this room. Nothing on this page is fetched or estimated; it is solved from the three dimensions in the URL.