Room Modes in an 11x28 ft Room with a 9 ft Ceiling

A 11 by 28 ft room with a 9 ft ceiling suits a dedicated home theater or media room. Its lowest room mode sits at 20.1 Hz, set by the 28 ft length, the lowest note the room itself reinforces before any speaker or sub plays a thing.

Checked against every mode below 200 Hz, this room scores 50/100, a rough score, worth planning around. The clearest issue is that two of its dimensions reinforce the same note near 100.5 Hz.

Lowest mode
20.1 Hz
Modes under 200 Hz
100
Schroeder frequency
143 Hz
Modal score
50/100

Mode spectrum

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

5 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 (28 ft)20.1 Hz40.2 Hz60.3 Hz80.4 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 20.1 Hz, set by the 28 ft length.
  • Your 28 ft length and 11 ft width both resonate near 100.5 Hz, so bass at that note will be much louder than its neighbours.
  • Your 28 ft length is almost exactly three times your 9 ft ceiling height, so their modes fall close together without quite stacking.
  • Between 20.1 Hz and 40.2 Hz there are no modes at all, so notes in that 20.1 Hz gap will sound thinner than the bass around them.
  • Mode density drops in the 25 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 : 3.11) fall outside the Bolt area because the room is long and narrow for its height, so modes bunch up along the length.
  • Below about 143 Hz (the Schroeder frequency) individual modes shape the sound; above it, reflections and reverb matter more.

The modes from your 28 ft length and 11 ft width land on top of each other near 100.5 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 : 3.11) 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. Put your first traps in the four vertical corners where floor meets ceiling; that is where every mode in this room reaches its loudest point, ceiling height included.
  2. Full absorption at 100.5 Hz would take about 2.8 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. Avoid the exact middle of the 28 ft length for your seat or mix position; try around 10.6 ft from the front wall (38% of the length) as a starting point, then nudge from there by ear.
  4. Test more than one subwoofer position. Corner placement drives the most output but also the least even bass; moving it along a wall or using two subs at different spots tends to average out this room’s peaks.
  5. Confirm the fix with an REW measurement at the listening position, paying closest attention below 143 Hz; above that, general room reverb matters more than any single mode.

These numbers assume an empty rectangular 11x28 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: 100 in all, 15 axial, 49 tangential and 36 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)
20.1 Hzaxial(1,0,0)
40.2 Hzaxial(2,0,0)
51.2 Hzaxial(0,1,0)
55 Hztangential(1,1,0)
60.3 Hzaxial(3,0,0)
62.5 Hzaxial(0,0,1)
65.1 Hztangential(2,1,0)
65.7 Hztangential(1,0,1)
74.3 Hztangential(2,0,1)
79.1 Hztangential(3,1,0)
80.4 Hzaxial(4,0,0)
80.8 Hztangential(0,1,1)
83.2 Hzoblique(1,1,1)
86.8 Hztangential(3,0,1)
90.2 Hzoblique(2,1,1)
95.3 Hztangential(4,1,0)
100.5 Hzaxial(5,0,0)
100.8 Hzoblique(3,1,1)
101.8 Hztangential(4,0,1)
102.3 Hzaxial(0,2,0)
104.3 Hztangential(1,2,0)
109.9 Hztangential(2,2,0)
112.7 Hztangential(5,1,0)
114 Hzoblique(4,1,1)
118.3 Hztangential(5,0,1)
118.7 Hztangential(3,2,0)
119.9 Hztangential(0,2,1)
120.6 Hzaxial(6,0,0)
121.6 Hzoblique(1,2,1)
125 Hzaxial(0,0,2)
126.4 Hzoblique(2,2,1)
126.6 Hztangential(1,0,2)
128.9 Hzoblique(5,1,1)
130.1 Hztangential(4,2,0)
131 Hztangential(6,1,0)
131.3 Hztangential(2,0,2)
134.2 Hzoblique(3,2,1)
135.1 Hztangential(0,1,2)
135.8 Hztangential(6,0,1)
136.6 Hzoblique(1,1,2)
138.8 Hztangential(3,0,2)
140.7 Hzaxial(7,0,0)
140.9 Hzoblique(2,1,2)
143.4 Hztangential(5,2,0)
144.3 Hzoblique(4,2,1)
145.1 Hzoblique(6,1,1)
147.9 Hzoblique(3,1,2)
148.6 Hztangential(4,0,2)
149.7 Hztangential(7,1,0)
153.5 Hzaxial(0,3,0)
153.9 Hztangential(7,0,1)
154.8 Hztangential(1,3,0)
156.4 Hzoblique(5,2,1)
157.2 Hzoblique(4,1,2)
158.1 Hztangential(6,2,0)
158.6 Hztangential(2,3,0)
160.4 Hztangential(5,0,2)
160.8 Hzaxial(8,0,0)
161.6 Hztangential(0,2,2)
162.2 Hzoblique(7,1,1)
162.8 Hzoblique(1,2,2)
164.9 Hztangential(3,3,0)
165.7 Hztangential(0,3,1)
166.5 Hzoblique(2,2,2)
166.9 Hzoblique(1,3,1)
168.4 Hzoblique(5,1,2)
168.7 Hztangential(8,1,0)
170 Hzoblique(6,2,1)
170.5 Hzoblique(2,3,1)
172.4 Hzoblique(3,2,2)
172.5 Hztangential(8,0,1)
173.2 Hztangential(4,3,0)
173.7 Hztangential(6,0,2)
173.9 Hztangential(7,2,0)
176.3 Hzoblique(3,3,1)
179.9 Hzoblique(8,1,1)
180.4 Hzoblique(4,2,2)
180.9 Hzaxial(9,0,0)
181.1 Hzoblique(6,1,2)
183.4 Hztangential(5,3,0)
184.2 Hzoblique(4,3,1)
184.8 Hzoblique(7,2,1)
187.6 Hzaxial(0,0,3)
188 Hztangential(9,1,0)
188.2 Hztangential(7,0,2)
188.6 Hztangential(1,0,3)
190.3 Hzoblique(5,2,2)
190.6 Hztangential(8,2,0)
191.4 Hztangential(9,0,1)
191.8 Hztangential(2,0,3)
193.8 Hzoblique(5,3,1)
194.4 Hztangential(0,1,3)
195 Hzoblique(7,1,2)
195.2 Hztangential(6,3,0)
195.4 Hzoblique(1,1,3)
197 Hztangential(3,0,3)
197.9 Hztangential(0,3,2)
198.1 Hzoblique(9,1,1)
198.5 Hzoblique(2,1,3)
199 Hzoblique(1,3,2)

Questions about 11x28 rooms

Is an 11 by 28 ft room good for a music room or home theater?
It can work as a dedicated home theater or media room, but do not expect an easy ride: this room scores 50/100 because two of its dimensions reinforce the same note near 100.5 Hz. Treatment will make a real difference here.
What is the best corner for bass traps in an 11x28 room?
The four vertical corners first. Full absorption at 100.5 Hz would take roughly 2.8 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 size subwoofer does an 11x28 room need?
Subwoofer size is less about this room's 308 sq ft and more about the output headroom you want; room size mainly changes where the 100 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 28 ft room?
Here it comes down to this: two of its dimensions reinforce the same note near 100.5 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 11x28 room?
Corner bass traps come first, as thick as you can fit (6 to 12 in) plus a membrane trap tuned near 100.5 Hz, since that note's own quarter wavelength (about 2.8 ft) is too deep for any panel. After that, reposition your seat near 10.6 ft from the front wall and verify with REW below 143 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.