Room Modes in a 13x28 ft Room with an 8 ft Ceiling

This 13x28 ft room, 8 ft to the ceiling, is a common size for a dedicated home theater or media room. Like any sealed box it resonates at fixed low notes; the lowest one lands at 20.1 Hz, driven by the 28 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 140.7 Hz.

Lowest mode
20.1 Hz
Modes under 200 Hz
105
Schroeder frequency
139 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 (13 ft)43.3 Hz86.6 Hz129.8 Hz173.1 Hz
Ceiling height (8 ft)70.3 Hz140.7 Hz211 Hz281.3 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 8 ft ceiling height both resonate at 140.7 Hz, so bass at that note will be much louder than its neighbours.
  • 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 and 50 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 : 1.63 : 3.50) fall outside the Bolt area because the room is long and narrow for its height, so modes bunch up along the length.
  • Below about 139 Hz (the Schroeder frequency) individual modes shape the sound; above it, reflections and reverb matter more.

Because your 28 ft length and 8 ft ceiling are close in size, their modes stack near 140.7 Hz. Expect that one note to sound louder, and ring longer, than the rest of the bass in this room.

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 stacked note. 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 : 1.63 : 3.50, 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. Start with bass traps in the four floor-to-ceiling corners; every mode in this room peaks there, including the ones set by your ceiling height.
  2. At 140.7 Hz the quarter wavelength is about 2 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. Do not sit dead-center on the 28 ft length. Start near 10.6 ft from the front wall, about 38% of the way back, and adjust from there.
  4. For the subwoofer, try a few spots before settling: a front corner usually gives the most output but also the most uneven bass, while pulling it off the wall or adding a second sub often smooths out peaks like the ones this room has.
  5. After treating, run an REW sweep from the seat. Everything below 139 Hz is where these modes live, so that is the range worth checking before you call the room done.

These numbers assume an empty rectangular 13x28 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

Below are all 105 modes this room produces under 200 Hz: 15 axial, 51 tangential, 39 oblique. Axial modes, which only involve one pair of opposite surfaces, ring the loudest. Tangential modes (four surfaces) come next, and oblique modes (all six surfaces) are the weakest of the three.

FrequencyTypeMode (length, width, height)
20.1 Hzaxial(1,0,0)
40.2 Hzaxial(2,0,0)
43.3 Hzaxial(0,1,0)
47.7 Hztangential(1,1,0)
59.1 Hztangential(2,1,0)
60.3 Hzaxial(3,0,0)
70.3 Hzaxial(0,0,1)
73.1 Hztangential(1,0,1)
74.2 Hztangential(3,1,0)
80.4 Hzaxial(4,0,0)
81 Hztangential(2,0,1)
82.6 Hztangential(0,1,1)
85 Hzoblique(1,1,1)
86.6 Hzaxial(0,2,0)
88.9 Hztangential(1,2,0)
91.3 Hztangential(4,1,0)
91.8 Hzoblique(2,1,1)
92.6 Hztangential(3,0,1)
95.4 Hztangential(2,2,0)
100.5 Hzaxial(5,0,0)
102.2 Hzoblique(3,1,1)
105.5 Hztangential(3,2,0)
106.8 Hztangential(4,0,1)
109.4 Hztangential(5,1,0)
111.5 Hztangential(0,2,1)
113.3 Hzoblique(1,2,1)
115.2 Hzoblique(4,1,1)
118.1 Hztangential(4,2,0)
118.6 Hzoblique(2,2,1)
120.6 Hzaxial(6,0,0)
122.6 Hztangential(5,0,1)
126.8 Hzoblique(3,2,1)
128.1 Hztangential(6,1,0)
129.8 Hzaxial(0,3,0)
130.1 Hzoblique(5,1,1)
131.4 Hztangential(1,3,0)
132.6 Hztangential(5,2,0)
135.9 Hztangential(2,3,0)
137.5 Hzoblique(4,2,1)
139.6 Hztangential(6,0,1)
140.7 Hzaxial(0,0,2)
140.7 Hzaxial(7,0,0)
142.1 Hztangential(1,0,2)
143.2 Hztangential(3,3,0)
146.1 Hzoblique(6,1,1)
146.3 Hztangential(2,0,2)
147.2 Hztangential(0,1,2)
147.2 Hztangential(7,1,0)
147.7 Hztangential(0,3,1)
148.4 Hztangential(6,2,0)
148.5 Hzoblique(1,1,2)
149 Hzoblique(1,3,1)
150.1 Hzoblique(5,2,1)
152.6 Hzoblique(2,1,2)
152.7 Hztangential(4,3,0)
153 Hztangential(3,0,2)
153 Hzoblique(2,3,1)
157.3 Hztangential(7,0,1)
159 Hzoblique(3,1,2)
159.5 Hzoblique(3,3,1)
160.8 Hzaxial(8,0,0)
162 Hztangential(4,0,2)
163.1 Hzoblique(7,1,1)
164.2 Hztangential(5,3,0)
164.2 Hzoblique(6,2,1)
165.2 Hztangential(0,2,2)
165.2 Hztangential(7,2,0)
166.4 Hzoblique(1,2,2)
166.5 Hztangential(8,1,0)
167.7 Hzoblique(4,1,2)
168.1 Hzoblique(4,3,1)
170 Hzoblique(2,2,2)
172.9 Hztangential(5,0,2)
173.1 Hzaxial(0,4,0)
174.3 Hztangential(1,4,0)
175.5 Hztangential(8,0,1)
175.8 Hzoblique(3,2,2)
177.2 Hztangential(6,3,0)
177.7 Hztangential(2,4,0)
178.2 Hzoblique(5,1,2)
178.6 Hzoblique(5,3,1)
179.5 Hzoblique(7,2,1)
180.7 Hzoblique(8,1,1)
180.9 Hzaxial(9,0,0)
182.6 Hztangential(8,2,0)
183.3 Hztangential(3,4,0)
183.7 Hzoblique(4,2,2)
185.3 Hztangential(6,0,2)
186 Hztangential(9,1,0)
186.9 Hztangential(0,4,1)
187.9 Hzoblique(1,4,1)
190.3 Hzoblique(6,1,2)
190.6 Hzoblique(6,3,1)
190.9 Hztangential(4,4,0)
191.1 Hzoblique(2,4,1)
191.4 Hztangential(0,3,2)
191.4 Hztangential(7,3,0)
192.5 Hzoblique(1,3,2)
193.3 Hzoblique(5,2,2)
194.1 Hztangential(9,0,1)
195.6 Hzoblique(2,3,2)
195.7 Hzoblique(8,2,1)
196.4 Hzoblique(3,4,1)
198.8 Hzoblique(9,1,1)
198.9 Hztangential(7,0,2)

Questions about 13x28 rooms

Is a 13x28 room good for a home theater?
At 364 sq ft, this size works as a dedicated home theater or media room, but a modal score of 50/100 means it is workable, not effortless: two of its dimensions reinforce the same note near 140.7 Hz, so plan on real bass trapping.
Where do bass traps go in a 13 by 28 ft room?
Start in the four floor-to-ceiling corners; every mode in this room peaks there. The 140.7 Hz mode itself would need about 2 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 140.7 Hz.
Do I need a big subwoofer for a 13x28 room?
Room size here mainly shapes where the modes land, not the sub size on its own; this room has 105 modes below 200 Hz to work around either way. Larger rooms like this one ask more of a subwoofer's output, and a second sub in a different spot helps smooth out the peaks and dips across seats.
Why does one bass note boom in a 13x28 room?
In this room, the main cause is that two of its dimensions reinforce the same note near 140.7 Hz. Room modes reinforce specific notes more than others no matter how good your speakers are, and that unevenness is what you are hearing.
How many bass traps does a 13 by 28 ft room need?
Start by treating the four corners with traps as thick as you can fit (6 to 12 in) plus a membrane trap tuned near 140.7 Hz, since that note's own quarter wavelength (about 2 ft) is too deep for any panel. Next, shift your listening position toward 10.6 ft from the front wall, then confirm progress with an REW sweep under 139 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.