Room Mode Calculator, RT60 and Bass-Trap Planner

For rigid rectangular boundaries, separation of the wave equation gives the Rayleigh eigenfrequencies

with nonnegative integer indices, excluding (0,0,0). One, two or three nonzero indices identify axial, tangential and oblique modes. Every candidate below the listing limit is counted, including multiplicities; the table shows the lowest 40. The workload guard prevents incomplete enumeration from being presented as a valid result.

The normalized pressure shape is $\cos(p\pi x/L)\cos(q\pi y/W)\cos(r\pi z/H)$. The map is a horizontal slice at the listener height. Phase playback multiplies this fixed shape by a cosine; it is slowed down and has no damping. Coupling outputs are absolute pressure-shape values, independent of phase.

Following Bonello (1981), count modes in third-octave bands near 10–200 Hz. Exact base-2 centers are $1000\,2^{k/3}$ for k = −20…−7, with edges $f_c2^{\pm1/6}$. This is an explicit screening convention rather than a copied standard table. We use the author's relaxed nondecreasing-density condition: equal successive counts are accepted. Repeated frequencies within 0.000001 Hz are flagged only in bands with fewer than five modes. These are geometric indicators, not a measure of audible response.

Per octave, $A=\sum S_i\alpha_i$, $S=\sum S_i$, $\bar\alpha=A/S$ and $V=LWH$. With the conventional coefficient $k=0.161$ s/m, $T_S=kV/A$ and $T_E=-kV/[S\ln(1-\bar\alpha)]$ (Lamancusa, attached source s3, p. 12, equations 9–10). Both estimates use the entered coefficients for comparison.

Treatment replaces a chosen finish: $A_{new}=A+a(\alpha_t-\alpha_h)$. The target absorption sum is $kV/T_{target}$ for Sabine or $S[1-\exp(-kV/(ST_{target}))]$ for Eyring. Divide a positive deficit by a positive coefficient gain to obtain the per-band required area. A nonpositive gain cannot remedy an above-target band; the table shows that status and zero positive-gain area. The proposed area is the largest positive-gain requirement capped at usable area; all bands are then recalculated, including any that worsen.

The Schroeder estimate is $f_s=2000\sqrt{T_{mid}/V}$ for seconds and cubic meters, with $T_{mid}$ the mean of the selected 500 Hz and 1 kHz predictions. It is computed before and after treatment (Linkwitz, section C2).

• A closed, rectangular room with rigid boundaries for mode frequencies; no openings, alcoves, sloped surfaces or coupled spaces.
• All four walls share their area-weighted coefficient. Floor and ceiling are separate. The seven coefficients in each group are user assumptions; the defaults are illustrative, not measured material data.
• As a broad guide, hard dense finishes are often around 0.01–0.10; lightweight panels can absorb more in bass. Porous treatment may range from weak bass absorption to strong mid/high absorption depending on thickness and mounting. Lamancusa (s3, pp. 2–5) explains this frequency dependence. Do not use these ranges as procurement data.
• Coefficients lie in 0…0.99. Eyring needs statistical energy-absorption coefficients; Sabine-derived chamber coefficients are not always interchangeable. Apparent measured coefficients above 1 are outside this area-averaged model and must not simply be entered as 1 or silently clipped.
• RT60 estimates assume a diffuse field and reasonably distributed absorption. Sabine is most useful for low absorption; Eyring represents larger mean absorption but does not cure poor diffusion.
• Surface absorption only: no air absorption, furniture, people or separately added object absorption. Predictions at high frequency may therefore be too long, especially in large rooms.
• The target is flat across all seven octaves and is chosen by the user. It is not a prescribed studio, classroom or regulatory limit.
• Gold markers represent two mirrored trial pressure traps at the slice height. Their size is schematic and unrelated to the sized treatment area. Mode geometry does not change when treatment is added.

Use for preliminary acoustic planning of rectangular rooms, not certification or final trap design. Modal frequency estimates assume lightly damped rigid boundaries; real flexible walls shift and damp resonances. Below the Schroeder estimate, isolated modal decays dominate and statistical RT60 has limited meaning; the bass-band estimates must not be read as predicted modal decay times.

A single-mode pressure maximum indicates possible coupling for a pressure-driven resonant absorber. Thin porous absorbers depend on particle velocity, thickness and air gap; a pressure antinode alone does not establish their effectiveness. The trap markers are independent location trials, not an optimized layout for the treatment coverage. Speaker position, directivity, phase, modal damping and boundary interference are absent, so neither listener nor trap coupling predicts total SPL or attenuation.

Bonello uses complete bands ending near 223 Hz, so the listing limit cannot be below 225 Hz. The input range is 1–20 m in length/width, 1–10 m in height, and 225–350 Hz in listing limit, subject to a maximum of 6,000 candidate index triples. No truncation is accepted beyond that guard.

A plan is successful only when every status reads Meets. If a band has no net gain or coverage is limited, change coefficients, available area or target and inspect the new predictions. Verify treatment performance with in-room measurements. Installation work belongs to a qualified person.