Room Modes in an 11x21 ft Room with an 8 ft Ceiling

This 11x21 ft room, 8 ft to the ceiling, is a common size for a bedroom theater or dedicated music room. Like any sealed box it resonates at fixed low notes; the lowest one lands at 26.8 Hz, driven by the 21 ft length.

On the 0-100 modal score, this room comes in at 55, a rough score, worth planning around. Before you treat anything, know that there is a gap of 24.4 Hz between 26.8 Hz and 51.2 Hz with no mode in between.

Lowest mode
26.8 Hz
Modes under 200 Hz
67
Schroeder frequency
175 Hz
Modal score
55/100

Mode spectrum

Mode spectrum · log frequency · stem height ≈ relative energy
Axial Tangential Oblique Cluster

6 dense clusters (≤5 Hz apart) — overlapping resonances are harder to treat evenly.

Each line is one standing wave. Axial modes, the strongest kind, stand tallest; tight bunches and wide empty stretches are where the bass will sound uneven.

Axial modes by dimension

Dimension1st2nd3rd4th
Length (21 ft)26.8 Hz53.6 Hz80.4 Hz107.2 Hz
Width (11 ft)51.2 Hz102.3 Hz153.5 Hz204.6 Hz
Ceiling height (8 ft)70.3 Hz140.7 Hz211 Hz281.3 Hz

What this means for your room

  • The lowest room mode is 26.8 Hz, set by the 21 ft length.
  • Your 21 ft length is almost exactly twice your 11 ft width, so their modes fall close together without quite stacking.
  • Between 26.8 Hz and 51.2 Hz there are no modes at all, so notes in that 24.4 Hz gap will sound thinner than the bass around them.
  • Mode density drops in the 31.5 and 63 Hz third-octave bands, where fewer modes fall than in the band below, so bass will sound uneven from note to note.
  • The proportions (1 : 1.38 : 2.63) fall outside the Bolt area because the room is long and narrow for its height, so modes bunch up along the length.
  • Below about 175 Hz (the Schroeder frequency) individual modes shape the sound; above it, reflections and reverb matter more.

No mode falls between 26.8 Hz and 51.2 Hz, a gap of 24.4 Hz. That is a spot where bass naturally loses energy instead of gaining it.

In a home theater, this shows up as one bass note in an action scene sounding far louder than the rest of the mix, usually a kick drum hit or an LFE cue landing right on that gap. In a music room, the same thing means certain bass notes on a track jump out while others next to them feel buried.

At 1 : 1.38 : 2.63, this room sits outside the Bolt area because the room is long and narrow for its height, which bunches modes up along the length. Expect to lean on bass traps and seat position a bit more than in a room with friendlier proportions.

How to fix it, in order

  1. Treat the four floor-to-ceiling corners first; they are common to every mode this room produces.
  2. Full absorption at 31.5 Hz would take about 8.9 ft of trap depth, well past what any room can fit. Fill the corners as deep as you reasonably can (6 to 12 in, with an air gap behind), then lean on a membrane trap tuned near that frequency, your seat position and a second subwoofer with EQ to tame the note itself.
  3. Move your listening position off-center along the 21 ft length; roughly 8 ft from the front wall (38% back) is a common starting spot before fine-tuning.
  4. Walk the subwoofer around the front of the room while playing a bass-heavy track and listen from your seat: corner placement is loudest but least even, and a second sub or an off-corner spot often fills in this room’s weak points.
  5. Once traps are in, measure with REW from the listening position. Focus on frequencies below 175 Hz (this room's Schroeder frequency); that is where individual modes, not general reverb, are running the show.

These numbers assume an empty rectangular 11x21 room with hard walls. Draw your real room, add furniture and speakers, and simulate the bass at your seat.

Model this room in 3D

Every mode below 200 Hz

The table below lists every mode under 200 Hz for this room: 67 in all, 12 axial, 33 tangential and 22 oblique. Axial modes bounce between just two parallel surfaces (say, the two side walls) and are the loudest and most audible; tangential modes involve four surfaces and are quieter; oblique modes bounce off all six surfaces and are the faintest. Start with the axial rows; they cause most of the boomy or thin spots you will actually hear.

FrequencyTypeMode (length, width, height)
26.8 Hzaxial(1,0,0)
51.2 Hzaxial(0,1,0)
53.6 Hzaxial(2,0,0)
57.7 Hztangential(1,1,0)
70.3 Hzaxial(0,0,1)
74.1 Hztangential(2,1,0)
75.3 Hztangential(1,0,1)
80.4 Hzaxial(3,0,0)
87 Hztangential(0,1,1)
88.4 Hztangential(2,0,1)
91 Hzoblique(1,1,1)
95.3 Hztangential(3,1,0)
102.2 Hzoblique(2,1,1)
102.3 Hzaxial(0,2,0)
105.8 Hztangential(1,2,0)
106.8 Hztangential(3,0,1)
107.2 Hzaxial(4,0,0)
115.5 Hztangential(2,2,0)
118.4 Hzoblique(3,1,1)
118.8 Hztangential(4,1,0)
124.1 Hztangential(0,2,1)
127 Hzoblique(1,2,1)
128.2 Hztangential(4,0,1)
130.1 Hztangential(3,2,0)
134 Hzaxial(5,0,0)
135.2 Hzoblique(2,2,1)
138 Hzoblique(4,1,1)
140.7 Hzaxial(0,0,2)
143.2 Hztangential(1,0,2)
143.4 Hztangential(5,1,0)
147.9 Hzoblique(3,2,1)
148.2 Hztangential(4,2,0)
149.7 Hztangential(0,1,2)
150.5 Hztangential(2,0,2)
151.3 Hztangential(5,0,1)
152.1 Hzoblique(1,1,2)
153.5 Hzaxial(0,3,0)
155.8 Hztangential(1,3,0)
159 Hzoblique(2,1,2)
159.7 Hzoblique(5,1,1)
160.8 Hzaxial(6,0,0)
162 Hztangential(3,0,2)
162.5 Hztangential(2,3,0)
164 Hzoblique(4,2,1)
168.6 Hztangential(5,2,0)
168.7 Hztangential(6,1,0)
168.8 Hztangential(0,3,1)
169.9 Hzoblique(3,1,2)
170.9 Hzoblique(1,3,1)
173.2 Hztangential(3,3,0)
173.9 Hztangential(0,2,2)
175.5 Hztangential(6,0,1)
176 Hzoblique(1,2,2)
176.8 Hztangential(4,0,2)
177.1 Hzoblique(2,3,1)
182 Hzoblique(2,2,2)
182.6 Hzoblique(5,2,1)
182.8 Hzoblique(6,1,1)
184.1 Hzoblique(4,1,2)
187 Hzoblique(3,3,1)
187.2 Hztangential(4,3,0)
187.6 Hzaxial(7,0,0)
190.6 Hztangential(6,2,0)
191.6 Hzoblique(3,2,2)
194.3 Hztangential(5,0,2)
194.4 Hztangential(7,1,0)
200 Hzoblique(4,3,1)

Questions about 11x21 rooms

Will an 11x21 room work for a home theater?
This size suits a bedroom theater or dedicated music room, though the 55/100 modal score signals some work ahead, mainly because there is a gap of 24.4 Hz between 26.8 Hz and 51.2 Hz with no mode in between.
Where should I put bass traps in an 11x21 room?
The four vertical corners first. Full absorption at 31.5 Hz would take roughly 8.9 ft of trap depth, so treat that note with a tuned membrane or pressure trap instead, and use thick porous corner traps (6 to 12 in) for everything above it.
What subwoofer size is right for an 11 by 21 ft room?
There is no fixed sub size tied to 231 sq ft; that number mostly sets this room's mode frequencies (67 of them under 200 Hz). At this size you will want more headroom than a small room needs, and two subwoofers usually beat one at keeping bass even from seat to seat.
Why does my 11x21 room have weak bass notes?
The short answer for this room: there is a gap of 24.4 Hz between 26.8 Hz and 51.2 Hz with no mode in between. Bass unevenness like that is built into the shape of the room and shows up regardless of what speakers or sub you use.
How do I fix bass problems in an 11x21 room?
Put bass traps in the four floor-to-ceiling corners first, as thick as you can fit (6 to 12 in) plus a membrane trap tuned near 31.5 Hz, since that note's own quarter wavelength (about 8.9 ft) is too deep for any panel. From there, move your seat to about 8 ft from the front wall, then measure with REW below 175 Hz to see what still needs work.

Similar room sizes

How these numbers are calculated

Modes use the rectangular-room equation f = (c/2)·√((nx/L)² + (ny/W)² + (nz/H)²) with c = 343 m/s, for an empty room with rigid walls. The Schroeder frequency is fs = 2000 x sqrt(RT60 / V), assuming RT60 = 0.4 s. The modal score starts at 100 and subtracts penalties for stacked modes, density dips, gaps, proportions outside the Bolt area and dimension multiples. Doors, openings and furniture shift real rooms away from these values, which is what the room mode calculator and the 3D editor are for.