Room Modes in an 11x21 ft Room with a 9 ft Ceiling

This 11x21 ft room, 9 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 50, a rough score, worth planning around. Before you treat anything, know that two of its dimensions reinforce the same note near 187.6 Hz.

Lowest mode
26.8 Hz
Modes under 200 Hz
77
Schroeder frequency
165 Hz
Modal score
50/100

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 (9 ft)62.5 Hz125 Hz187.6 Hz250.1 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.
  • Your 21 ft length and 9 ft ceiling height both resonate at 187.6 Hz, so bass at that note will be much louder than its neighbours.
  • 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 Hz third-octave band (0 modes against 1 in the band below), so bass will sound uneven from note to note.
  • The proportions (1 : 1.22 : 2.33) fall outside the Bolt area because the room is long and narrow for its height, so modes bunch up along the length.
  • Below about 165 Hz (the Schroeder frequency) individual modes shape the sound; above it, reflections and reverb matter more.

The modes from your 21 ft length and 9 ft ceiling land on top of each other near 187.6 Hz. That stack means one specific low note gets reinforced twice, so it jumps out over everything nearby.

For a home theater, expect that stacked note to color explosions and sub-bass hits unevenly rather than smoothly. For a music room, it means you cannot fully trust what you hear in the low end at the listening position, since a note that sounds loud in the room may be perfectly balanced on the recording.

The proportions (1 : 1.22 : 2.33) fall outside the Bolt area, the range room ratios usually spread modes best over, because the room is long and narrow for its height, which bunches modes up along the length. That does not rule the room out, but treatment is doing more of the work here than shape is.

How to fix it, in order

  1. Treat the four floor-to-ceiling corners first; they are common to every mode this room produces, and your ceiling height is part of the problem.
  2. At 187.6 Hz the quarter wavelength is about 1.5 ft, deeper than any practical panel, so a porous trap alone will not fully absorb that note. Build corner traps as thick as you can fit (6 to 12 in, straddling the corner with an air gap behind) to take the edge off, then handle the note itself with a membrane or pressure trap tuned near it, careful seat position, and more than one subwoofer with EQ.
  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 165 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

This room has 77 modes below 200 Hz, 13 axial, 38 tangential and 26 oblique. Read the axial rows as the ones you will hear most clearly. Tangential and oblique modes add texture but usually only become audible when they land close to an axial mode.

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)
62.5 Hzaxial(0,0,1)
68 Hztangential(1,0,1)
74.1 Hztangential(2,1,0)
80.4 Hzaxial(3,0,0)
80.8 Hztangential(0,1,1)
82.3 Hztangential(2,0,1)
85.1 Hzoblique(1,1,1)
95.3 Hztangential(3,1,0)
96.9 Hzoblique(2,1,1)
101.8 Hztangential(3,0,1)
102.3 Hzaxial(0,2,0)
105.8 Hztangential(1,2,0)
107.2 Hzaxial(4,0,0)
114 Hzoblique(3,1,1)
115.5 Hztangential(2,2,0)
118.8 Hztangential(4,1,0)
119.9 Hztangential(0,2,1)
122.9 Hzoblique(1,2,1)
124.1 Hztangential(4,0,1)
125 Hzaxial(0,0,2)
127.9 Hztangential(1,0,2)
130.1 Hztangential(3,2,0)
131.3 Hzoblique(2,2,1)
134 Hzaxial(5,0,0)
134.2 Hzoblique(4,1,1)
135.1 Hztangential(0,1,2)
136 Hztangential(2,0,2)
137.7 Hzoblique(1,1,2)
143.4 Hztangential(5,1,0)
144.3 Hzoblique(3,2,1)
145.3 Hzoblique(2,1,2)
147.8 Hztangential(5,0,1)
148.2 Hztangential(4,2,0)
148.6 Hztangential(3,0,2)
153.5 Hzaxial(0,3,0)
155.8 Hztangential(1,3,0)
156.4 Hzoblique(5,1,1)
157.2 Hzoblique(3,1,2)
160.8 Hzaxial(6,0,0)
160.8 Hzoblique(4,2,1)
161.6 Hztangential(0,2,2)
162.5 Hztangential(2,3,0)
163.8 Hzoblique(1,2,2)
164.7 Hztangential(4,0,2)
165.7 Hztangential(0,3,1)
167.9 Hzoblique(1,3,1)
168.6 Hztangential(5,2,0)
168.7 Hztangential(6,1,0)
170.2 Hzoblique(2,2,2)
172.4 Hzoblique(4,1,2)
172.5 Hztangential(6,0,1)
173.2 Hztangential(3,3,0)
174.1 Hzoblique(2,3,1)
179.8 Hzoblique(5,2,1)
179.9 Hzoblique(6,1,1)
180.4 Hzoblique(3,2,2)
183.3 Hztangential(5,0,2)
184.2 Hzoblique(3,3,1)
187.2 Hztangential(4,3,0)
187.6 Hzaxial(0,0,3)
187.6 Hzaxial(7,0,0)
189.5 Hztangential(1,0,3)
190.3 Hzoblique(5,1,2)
190.6 Hztangential(6,2,0)
193.9 Hzoblique(4,2,2)
194.4 Hztangential(0,1,3)
194.4 Hztangential(7,1,0)
195.1 Hztangential(2,0,3)
196.2 Hzoblique(1,1,3)
197.3 Hzoblique(4,3,1)
197.7 Hztangential(7,0,1)
197.9 Hztangential(0,3,2)
199.8 Hzoblique(1,3,2)

Questions about 11x21 rooms

Is an 11 by 21 ft room good for a music room or home theater?
It can work as a bedroom theater or dedicated music room, but do not expect an easy ride: this room scores 50/100 because two of its dimensions reinforce the same note near 187.6 Hz. Treatment will make a real difference here.
What is the best corner for bass traps in an 11x21 room?
Start in the four floor-to-ceiling corners; every mode in this room peaks there. The 187.6 Hz mode itself would need about 1.5 ft of depth to fully absorb, more than any panel can give, so build corner traps as thick as you can fit (6 to 12 in) and pair them with a membrane trap tuned near 187.6 Hz.
What size subwoofer does an 11x21 room need?
Subwoofer size is less about this room's 231 sq ft and more about the output headroom you want; room size mainly changes where the 77 modes below 200 Hz fall. A room this size needs more sub output to reach the same level as a smaller one, and running two subs at different spots evens out the response between seats.
Why is bass boomy in one spot in an 11 by 21 ft room?
Here it comes down to this: two of its dimensions reinforce the same note near 187.6 Hz. That is a property of the room's shape, not your equipment, so treatment, not a better sub, is the fix.
What is the fastest fix for bass in an 11x21 room?
Corner bass traps come first, as thick as you can fit (6 to 12 in) plus a membrane trap tuned near 187.6 Hz, since that note's own quarter wavelength (about 1.5 ft) is too deep for any panel. After that, reposition your seat near 8 ft from the front wall and verify with REW below 165 Hz.

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.