Room Modes in a 13x17 ft Room with a 10 ft Ceiling

At 13 by 17 ft with a 10 ft ceiling, this room works well as a bedroom theater or dedicated music room. Its first room mode, the lowest note the walls naturally reinforce, falls at 33.1 Hz, set by the 17 ft length.

That puts its modal score at 64 out of 100, a decent score, typical for a room this shape. The main thing to plan around: two of its dimensions reinforce the same note near 129.8 Hz.

Lowest mode
33.1 Hz
Modes under 200 Hz
81
Schroeder frequency
160 Hz
Modal score
64/100

Mode spectrum

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

8 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 (17 ft)33.1 Hz66.2 Hz99.3 Hz132.4 Hz
Width (13 ft)43.3 Hz86.6 Hz129.8 Hz173.1 Hz
Ceiling height (10 ft)56.3 Hz112.5 Hz168.8 Hz225.1 Hz

What this means for your room

  • The lowest room mode is 33.1 Hz, set by the 17 ft length.
  • Your 17 ft length and 13 ft width both resonate near 129.8 Hz, so bass at that note will be much louder than its neighbours.
  • Your 17 ft length and 10 ft ceiling height both resonate near 165.5 Hz, so bass at that note will be much louder than its neighbours.
  • Your 13 ft width and 10 ft ceiling height both resonate near 168.8 Hz, so bass at that note will be much louder than its neighbours.
  • Between 43.3 Hz and 54.5 Hz there are no modes at all, so notes in that 11.2 Hz gap will sound thinner than the bass around them.
  • The proportions (1 : 1.30 : 1.70) fall inside the Bolt area, the range of room ratios that spreads modes most evenly.
  • Below about 160 Hz (the Schroeder frequency) individual modes shape the sound; above it, reflections and reverb matter more.

Your 17 ft length and 13 ft width share a mode near 129.8 Hz. When two dimensions resonate at the same note, their boosts add up, so that note stacks on top of itself and comes out noticeably louder than the bass around it.

If you use this room for movies, that stacked note tends to show up as boom on specific low-frequency effects rather than an even rumble. If it is a music or mixing room, that same spot makes some bass notes read louder on playback than they actually are on the recording, which makes mixing bass by ear risky here.

Height, width and length work out to 1 : 1.30 : 1.70, which lands inside the Bolt area. Rooms with that proportion usually need less correction than a room shaped like a cube or a hallway.

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. Full absorption at 129.8 Hz would take about 2.2 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. Do not sit dead-center on the 17 ft length. Start near 6.5 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 160 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 13x17 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 81 modes this room produces under 200 Hz: 13 axial, 38 tangential, 30 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)
33.1 Hzaxial(1,0,0)
43.3 Hzaxial(0,1,0)
54.5 Hztangential(1,1,0)
56.3 Hzaxial(0,0,1)
65.3 Hztangential(1,0,1)
66.2 Hzaxial(2,0,0)
71 Hztangential(0,1,1)
78.3 Hzoblique(1,1,1)
79.1 Hztangential(2,1,0)
86.6 Hzaxial(0,2,0)
86.9 Hztangential(2,0,1)
92.7 Hztangential(1,2,0)
97.1 Hzoblique(2,1,1)
99.3 Hzaxial(3,0,0)
103.2 Hztangential(0,2,1)
108.3 Hztangential(3,1,0)
108.4 Hzoblique(1,2,1)
109 Hztangential(2,2,0)
112.5 Hzaxial(0,0,2)
114.1 Hztangential(3,0,1)
117.3 Hztangential(1,0,2)
120.6 Hztangential(0,1,2)
122.1 Hzoblique(3,1,1)
122.6 Hzoblique(2,2,1)
125 Hzoblique(1,1,2)
129.8 Hzaxial(0,3,0)
130.6 Hztangential(2,0,2)
131.7 Hztangential(3,2,0)
132.4 Hzaxial(4,0,0)
134 Hztangential(1,3,0)
137.5 Hzoblique(2,1,2)
139.3 Hztangential(4,1,0)
141.5 Hztangential(0,3,1)
142 Hztangential(0,2,2)
143.2 Hzoblique(3,2,1)
143.9 Hztangential(4,0,1)
145.3 Hzoblique(1,3,1)
145.7 Hztangential(2,3,0)
145.8 Hzoblique(1,2,2)
150.1 Hztangential(3,0,2)
150.2 Hzoblique(4,1,1)
156.2 Hzoblique(2,3,1)
156.2 Hzoblique(3,1,2)
156.6 Hzoblique(2,2,2)
158.2 Hztangential(4,2,0)
163.5 Hztangential(3,3,0)
165.5 Hzaxial(5,0,0)
167.9 Hzoblique(4,2,1)
168.8 Hzaxial(0,0,3)
171.1 Hztangential(5,1,0)
171.8 Hztangential(0,3,2)
172 Hztangential(1,0,3)
172.9 Hzoblique(3,3,1)
173.1 Hzaxial(0,4,0)
173.3 Hzoblique(3,2,2)
173.8 Hztangential(4,0,2)
174.3 Hztangential(0,1,3)
174.8 Hztangential(5,0,1)
175 Hzoblique(1,3,2)
176.3 Hztangential(1,4,0)
177.4 Hzoblique(1,1,3)
179.1 Hzoblique(4,1,2)
180.1 Hzoblique(5,1,1)
181.3 Hztangential(2,0,3)
182 Hztangential(0,4,1)
184.1 Hzoblique(2,3,2)
185 Hzoblique(1,4,1)
185.4 Hztangential(2,4,0)
185.4 Hztangential(4,3,0)
186.4 Hzoblique(2,1,3)
186.8 Hztangential(5,2,0)
189.7 Hztangential(0,2,3)
192.6 Hzoblique(1,2,3)
193.7 Hzoblique(2,4,1)
193.8 Hzoblique(4,3,1)
194.1 Hzoblique(4,2,2)
195.1 Hzoblique(5,2,1)
195.8 Hztangential(3,0,3)
198.5 Hzoblique(3,3,2)
198.6 Hzaxial(6,0,0)
199.6 Hztangential(3,4,0)

Questions about 13x17 rooms

Will a 13x17 room work for a home theater?
This size suits a bedroom theater or dedicated music room, though the 64/100 modal score signals some work ahead, mainly because two of its dimensions reinforce the same note near 129.8 Hz.
Where should I put bass traps in a 13x17 room?
The four vertical corners first. Full absorption at 129.8 Hz would take roughly 2.2 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 a 13 by 17 ft room?
There is no fixed sub size tied to 221 sq ft; that number mostly sets this room's mode frequencies (81 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 13x17 room have one loud bass note?
The short answer for this room: two of its dimensions reinforce the same note near 129.8 Hz. 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 a 13x17 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 129.8 Hz, since that note's own quarter wavelength (about 2.2 ft) is too deep for any panel. From there, move your seat to about 6.5 ft from the front wall, then measure with REW below 160 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.