Index Room & AcousticsRoom Modes

Room Modes

Standing-wave frequencies of a rectangular room and where they pile up.

Lowest mode33Hz

Schroeder frequency178Hz

Closest axial pair132 / 132Hzmodes pile up here

Volume50.7m³

Modes up to 300 Hz

Axial (two walls)
Tangential (four)
Oblique (all six)

Even spacing is good. Gaps and clusters mean some bass notes boom while others vanish.

First axial modes

Frequency	Between	Order	Half waves
33.0 Hz	length	(1,0,0)	1
44.0 Hz	width	(0,1,0)	1
66.0 Hz	length	(2,0,0)	2
68.6 Hz	height	(0,0,1)	1
87.9 Hz	width	(0,2,0)	2
98.9 Hz	length	(3,0,0)	3
131.9 Hz	length	(4,0,0)	4
131.9 Hz	width	(0,3,0)	3
137.2 Hz	height	(0,0,2)	2
164.9 Hz	length	(5,0,0)	5

Input

Length

L

Width

W

Height

H

Reverberation time

T_{60}

Only used for the Schroeder frequency. 0.3 to 0.5 s is typical for a furnished room.

How it works

Standing waves

Between two parallel walls, sound whose half wavelength fits a whole number of times reinforces itself on every bounce. In a rectangular room the full set of resonances is

f_{p,q,r} = \frac{c}{2}\sqrt{\left(\frac{p}{L}\right)^{2} + \left(\frac{q}{W}\right)^{2} + \left(\frac{r}{H}\right)^{2}}

where $p, q, r$ are whole numbers counting half waves along each dimension.

Axial modes have one non-zero index and bounce between two facing surfaces. They are the strongest.
Tangential modes involve four surfaces and carry about half the energy.
Oblique modes touch all six and are weaker still.

Where modes stop mattering

Higher up, modes overlap so densely that the room behaves statistically and individual resonances are no longer heard. The crossover between the two regimes is the Schroeder frequency:

f_S \approx 2000\sqrt{\frac{T_{60}}{V}}

with volume in cubic metres. Below it, placement and bass trapping matter; above it, absorption and diffusion do.

Reading the result

Dimensions that are equal or simple multiples of each other stack their modes on the same frequencies. Try a 4 × 4 × 2.5 m room to see it. You cannot move walls, but you can move the seat: sitting at a quarter or a third of the room length avoids the pressure nulls of the lowest modes.

References

M. R. Schroeder, “Die statistischen Parameter der Frequenzkurven von großen Räumen,” Acustica, vol. 4, pp. 594–600, 1954. English translation: “Statistical Parameters of the Frequency Response Curves of Large Rooms,” J. Audio Eng. Soc., vol. 35, no. 5, pp. 299–306, 1987. AES
M. R. Schroeder, “The ‘Schroeder frequency’ revisited,” J. Acoust. Soc. Am., vol. 99, no. 5, pp. 3240–3241, 1996. ASA

Frequency

Between

Order

Half waves

33.0 Hz

length

(1,0,0)

44.0 Hz

width

(0,1,0)

66.0 Hz

length

(2,0,0)

68.6 Hz

height

(0,0,1)

87.9 Hz

width

(0,2,0)

98.9 Hz

length

(3,0,0)

131.9 Hz

length

(4,0,0)

131.9 Hz

width

(0,3,0)

137.2 Hz

height

(0,0,2)

164.9 Hz

length

(5,0,0)

How it works

Standing waves

Between two parallel walls, sound whose half wavelength fits a whole number of times reinforces itself on every bounce. In a rectangular room the full set of resonances is

f_{p,q,r} = \frac{c}{2}\sqrt{\left(\frac{p}{L}\right)^{2} + \left(\frac{q}{W}\right)^{2} + \left(\frac{r}{H}\right)^{2}}

where $p, q, r$ are whole numbers counting half waves along each dimension.

Axial modes have one non-zero index and bounce between two facing surfaces. They are the strongest.
Tangential modes involve four surfaces and carry about half the energy.
Oblique modes touch all six and are weaker still.

Where modes stop mattering

Higher up, modes overlap so densely that the room behaves statistically and individual resonances are no longer heard. The crossover between the two regimes is the Schroeder frequency:

f_S \approx 2000\sqrt{\frac{T_{60}}{V}}

with volume in cubic metres. Below it, placement and bass trapping matter; above it, absorption and diffusion do.

Reading the result

References

M. R. Schroeder, “Die statistischen Parameter der Frequenzkurven von großen Räumen,” Acustica, vol. 4, pp. 594–600, 1954. English translation: “Statistical Parameters of the Frequency Response Curves of Large Rooms,” J. Audio Eng. Soc., vol. 35, no. 5, pp. 299–306, 1987. AES
M. R. Schroeder, “The ‘Schroeder frequency’ revisited,” J. Acoust. Soc. Am., vol. 99, no. 5, pp. 3240–3241, 1996. ASA