Boundary Cancellation and Room Modes

If you have a cancellation at a given frequency, this chart will tell you the distance from the speaker to the boundary that is causing the cancellation. In addition, if you measure the distance from a speaker to a boundary, this chart will tell you the frequency at which that boundary will cause a cancellation.

Freq	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100	105
Feet	28.25	18.83	14.13	11.30	9.42	8.07	7.06	6.28	5.65	5.14	4.71	4.35	4.04	3.77	3.53	3.32	3.14	2.97	2.83	2.69
Inches	339.00	226.00	169.50	135.60	113.00	96.86	84.75	75.33	67.80	61.64	56.50	52.15	48.43	45.20	42.38	39.88	37.67	35.68	33.90	32.29

Freq	110	115	120	125	130	135	140	145	150	155	160	165	170	175	180	185	190	195	200	205
Feet	2.57	2.46	2.35	2.26	2.17	2.09	2.02	1.95	1.88	1.82	1.77	1.71	1.66	1.61	1.57	1.53	1.49	1.45	1.41	1.38
Inches	30.82	29.48	28.25	27.12	26.08	25.11	24.21	23.38	22.60	21.87	21.19	20.55	19.94	19.37	18.83	18.32	17.84	17.38	16.95	16.54

Freq	210	215	220	225	230	235	240	245	250	255	260	265	270	275	280	285	290	295	300	305
Feet	1.35	1.31	1.28	1.26	1.23	1.20	1.18	1.15	1.13	1.11	1.09	1.07	1.05	1.03	1.01	0.99	0.97	0.96	0.94	0.93
Inches	16.14	15.77	15.41	15.07	14.74	14.43	14.13	13.84	13.56	13.29	13.04	12.79	12.56	12.33	12.11	11.89	11.69	11.49	11.30	11.11

Freq	310	315	320	325	330	335	340	345	350	355	360	365	370	375	380	385	390	395	400	405
Feet	0.91	0.90	0.88	0.87	0.86	0.84	0.83	0.82	0.81	0.80	0.78	0.77	0.76	0.75	0.74	0.73	0.72	0.72	0.71	0.70
Inches	10.94	10.76	10.59	10.43	10.27	10.12	9.97	9.83	9.69	9.55	9.42	9.29	9.16	9.04	8.92	8.81	8.69	8.58	8.48	8.37

Freq	410	415	420	425	430	435	440	445	450	455	460	465	470	475	480	485	490	495	500	505
Feet	0.69	0.68	0.67	0.66	0.66	0.65	0.64	0.63	0.63	0.62	0.61	0.61	0.60	0.59	0.59	0.58	0.58	0.57	0.57	0.56
Inches	8.27	8.17	8.07	7.98	7.88	7.79	7.70	7.62	7.53	7.45	7.37	7.29	7.21	7.14	7.06	6.99	6.92	6.85	6.78	6.71

Every enclosed space has natural resonances, called Room Modes. This chart will tell you the frequency at which a given dimension will resonate. Note that each given dimension will also resonate 2x, 4x, 8x, etc. the frequency of the main mode. (It's actually much more complicated than this - see the calculator javascript at http://www.mcsquared.com/modecalc.htm or http://www.mcsquared.com/metricmodes.htm)

Feet	70	69	68	67	66	65	64	63	62	61	60	59	58	57	56	55	54	53	52	51
Freq	8.07	8.19	8.31	8.43	8.56	8.69	8.83	8.97	9.11	9.26	9.42	9.58	9.74	9.91	10.09	10.27	10.46	10.66	10.87	11.08

Feet	50	49	48	47	46	45	44	43	42	41	40	39	38	37	36	35	34	33	32	31
Freq	11.30	11.53	11.77	12.02	12.28	12.56	12.84	13.14	13.45	13.78	14.13	14.49	14.87	15.27	15.69	16.14	16.62	17.12	17.66	18.23

Feet	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16.5	16	15.5	15	14.5	14
Freq	18.83	19.48	20.18	20.93	21.73	22.60	23.54	24.57	25.68	26.90	28.25	29.74	31.39	33.24	34.24	35.31	36.45	37.67	38.97	40.36

Feet	13.5	13	12.5	12	11.5	11	10.5	10	9.5	9	8.5	8	7.5	7	6.5	6	5.5	5	4.5	4
Freq	41.85	43.46	45.20	47.08	49.13	51.36	53.81	56.50	59.47	62.78	66.47	70.63	75.33	80.71	86.92	94.17	102.73	113.00	125.56	141.25

What use is all this? Say you have a boom at about 70 Hz. This is the first mode of 8', a common ceiling height. (And the octave of the first mode of ~16'.) Looking at the Boundary Cancellation Charts, we find that a 70Hz cancellation occurs at ~ 48.5". Put the bass driver(s) at 48.5" from a boundary and see what happens.
Going the other way, say we cannot place the bass drivers against a boundary, but we have some choice as to where they can go. Try a spot whose boundary cancellation matches a resonance mode. Say we have a 12' ceiling. The first mode will be at 47Hz. The cancellation distance for 47Hz is ~6'. If the drivers can go 6' from the wall or floor, try them there.