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Room Acoustics

Room Modes & Standing Waves

Explore low-frequency resonances in a rectangular room. Mode indices select an eigenfrequency and its pressure pattern; surface materials determine the separate reverberation estimate.

Room Dimensions
Length Lx (m)
m
Width Ly (m)
m
Height Lz (m)
m
Absorber Preset
Floor Material
Wall Material
Ceiling Material
Results
Results
—
RT60 mid-band (s)
—
Volume V (m³)
—
Schroeder fc (Hz)
—
Displayed modes (≤500 Hz)
RT60
(1,0,0)
Mode (nx,ny,nz)
—
Mode frequency (Hz)
—
RT60 Sabine (s)
—
Total absorption A (m²sabin)
Speed1.0×
Sound pressure (high ↔ low) Nodal line (zero sound pressure) Reverberant energy
Rt60
Theory & Key Formulas
$$RT_{60}= \frac{0.161\,V}{\sum \alpha_i S_i}$$ $$f_n = \frac{c}{2}\sqrt{\left(\frac{n_x}{L_x}\right)^2+\left(\frac{n_y}{L_y}\right)^2+\left(\frac{n_z}{L_z}\right)^2}$$ $$f_s \approx 2000\sqrt{\frac{RT_{60}}{V}}$$

Inputs and readouts

Lx, Ly and Lz are internal length, width and height in metres. Floor and ceiling each have area Lx×Ly; wall area includes all four walls. Material menus select stored absorption coefficients at 125, 250, 500, 1000, 2000 and 4000 Hz. Custom coefficients, furniture, occupants and material thickness are not inputs.

Mid-band RT60 is the arithmetic mean of the 500 Hz and 1000 Hz results. Absorption A is the 500 Hz equivalent absorption area, not a band average. Bar colours are visual categories, not pass/fail ratings.

Reproducible examples

Default room: 8×6×3 m, carpet floor, concrete walls and acoustic ceiling. V=144 m³. At 500 Hz the coefficients are 0.14, 0.02 and 0.78: A=48×0.14+84×0.02+48×0.78=45.84 m². RT60(500 Hz)=0.161×144/45.84=0.506 s; at 1000 Hz it is 0.370 s. Mid-band RT60 rounds to 0.44 s and the Schroeder estimate to 110 Hz.

Keep 8×6×3 m and select concrete for every surface. At both 500 and 1000 Hz, α=0.02. Total surface area is 180 m² and A=3.60 m², giving mid-band RT60=6.44 s and a Schroeder estimate of 423 Hz. Less absorption gives a longer reverberant decay.

With sound speed 343 m/s, mode (1,0,0) in the default room is 343/(2×8)=21.44 Hz. Doubling only Lx to 16 m lowers it to 10.72 Hz. Selecting another mode changes the observed pattern, not the material-based RT60.

Model and limits

Sabine RT60 is a diffuse-field estimate. Strong or uneven absorption and low frequencies in small rooms can depart substantially from this model. Stored material values are illustrative, not certified data for a particular product, thickness or installation. Air absorption, openings, furniture, occupants and sound insulation are excluded. Check product test data and measurement conditions for actual designs.

Modes assume a rigid rectangular room and sound speed 343 m/s. The displayed set is limited to nx=0–6, ny=0–6, nz=0–4 and frequencies ≤500 Hz, excluding (0,0,0). The count is this low-order subset, not all modes below 500 Hz. Different index combinations at the same frequency count separately.

The standing-wave plan depicts the z=0 plane. Changing nz changes frequency, but vertical nodes are not drawn in this slice. Animation speed affects the display only, not the eigenfrequency or RT60.

V = Lx·Ly·Lz; A(f) = Σ Sᵢαᵢ(f); T₆₀(f) = 0.161 V / A(f); fₛ ≈ 2000 √(Tmid / V).

f(nx,ny,nz) = (343/2) √[(nx/Lx)² + (ny/Ly)² + (nz/Lz)²].

Frequently asked questions

Does this calculator compare Sabine and Eyring?

No. The numerical results and octave-band chart use Sabine only. Eyring is not implemented, so the display must not be read as a comparison of the two models.

Are mid-band RT60 and absorption A at the same frequency?

Mid-band RT60 averages the 500 Hz and 1000 Hz reverberation times. A is the 500 Hz absorption area; use the 500 Hz RT60 when checking the formula against A.

Does the count include every mode below 500 Hz?

No. Only indices nx and ny from 0 to 6 and nz from 0 to 4 are included. Larger rooms have more modes outside these limits; this is not a total mode count.

Can the results approve an acoustic design?

No. Reverberation time is one acoustic measure. Seat-dependent levels, speech clarity, insulation and flutter echoes need suitable measurements or more detailed analysis.

References