Double-Wall Sound Transmission Loss (TL) Simulator

Calculate the sound transmission loss of a "two panels + air gap" construction — double-glazed windows, studio partitions, speaker enclosures. Vary the surface mass, air-gap thickness, cavity absorber and analysis frequency to see the mass-air-mass (MAM) resonance dip at low frequencies and the dramatic improvement above it.

Parameters

Wall 1 surface mass m₁

kg/m²

Outer-leaf surface mass (12 mm gypsum board ≈ 10, 6 mm glass ≈ 15)

Wall 2 surface mass m₂

kg/m²

Inner-leaf surface mass. Making it differ from m₁ splits the resonance.

Air-gap thickness d

A wider gap lowers fMAM and improves low-frequency insulation.

Cavity damping

Glasswool / mineral-wool fill ratio. Damps the MAM dip.

Analysis frequency f

Single frequency at which the headline TL is evaluated.

Structural bridging

Rigid coupling via studs/bolts. 0 = independent studs, 1 = direct.

Results

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Wall 1 single TL (dB)

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Wall 2 single TL (dB)

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MAM resonance freq. (Hz)

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Double-wall TL (dB)

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STC estimate (dB)

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Gain vs single wall (dB)

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Double-wall section — sound-wave visualization

Incident sound (left) traverses the outer leaf, the air cavity and the inner leaf, emerging strongly attenuated on the right. Streaks inside the cavity indicate panel vibration at the MAM resonance.

TL vs frequency — single wall vs double wall

MAM resonance vs air-gap thickness

Theory & Key Formulas

$$TL_{single} = 20\log_{10}(mf) - 47.4,\quad f_{MAM} = \frac{1}{2\pi}\sqrt{\frac{\rho c^2}{d}\left(\frac{1}{m_1}+\frac{1}{m_2}\right)}$$

m = surface mass (kg/m²), f = frequency (Hz), d = air-gap thickness (m), ρ = air density, c = sound speed. Above MAM the TL grows at +12 dB/octave.

$$TL_{double} \approx TL_1 + TL_2 + 20\log_{10}(d/d_{ref})\quad (f \gg f_{MAM})$$

Well above the MAM resonance the two single-wall losses and the air-gap term add up, giving a large improvement over a single panel.

Double-Wall Transmission Loss and the Mass-Air-Mass Resonance

🙋

I doubled up the wall of my DIY home studio and now my neighbour says only the bass leaks through. I thought a double wall was supposed to fix everything?

🎓

You ran straight into the mass-air-mass (MAM) resonance. Physically a double wall is a "mass (panel 1) — spring (air) — mass (panel 2)" oscillator, and every spring-mass system has a natural frequency. At that frequency the two panels swing out of phase and the air cavity pumps sound across like a piston, so the TL actually drops below the single-wall value. That is the "dip" you are hearing in the bass.

🙋

So a double wall can be worse than a single one at some frequencies?! How do I work out where that resonance lands?

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The formula is fMAM = (1/2π)·sqrt((ρc²/d)·(1/m₁+1/m₂)), with ρ = 1.225 kg/m³, c = 343 m/s, d in metres and m₁, m₂ as surface masses. Two 12 mm gypsum boards (≈10 kg/m² each) over a 50 mm cavity put fMAM around 100 Hz — right where kick drums live. The default in this tool (m = 15, d = 100 mm) gives fMAM ≈ 70 Hz, which keeps the dip well below the main vocal band.

🙋

How do I push that MAM dip down? Increasing the air gap looks like it would help…

🎓

Three knobs work. (1) Widen the air gap d (fMAM ∝ 1/√d, so 4× the gap halves the resonance). (2) Raise the panel mass m₁, m₂ (heavier boards, or a lead sandwich). (3) Fill the cavity with glasswool — slide the "Cavity damping" control from 0 to 70 % and watch the dip become shallower. In practice, gap + absorber is the most cost-effective combination.

🙋

What is the "structural bridging" slider doing?

🎓

That models flanking — the indirect path through the wood or metal studs that physically connect the two leaves. Sound takes a shortcut through that bridge. Almost every case of "I computed 55 dB but I measure 40 dB" is flanking. Professional studios fix it with staggered or fully independent studs and "sound isolation clips" that break the rigid coupling. A bridging of 0 is ideal; 0.5 is the typical cheap-DIY wall.

🙋

I keep hearing about STC. It shows up here too — what is it?

🎓

STC (Sound Transmission Class) is a single-number rating derived by fitting a reference curve over the 125–4000 Hz TL data. Houses usually sit at 30–40, recording studios at 50–60. This tool approximates it as the 125–2000 Hz average of the mass-law TL; real lab STC tends to come in 5–10 dB lower because of the MAM dip and coincidence effects. Design with a "target STC + 5 dB" margin to be safe.

Frequently Asked Questions

A double wall can be modelled as two masses (the panels) coupled by a spring (the trapped air), and its natural frequency is called the mass-air-mass resonance. It is given by fMAM = (1/2π)·sqrt((ρc²/d)(1/m₁+1/m₂)) and typically falls between 80 and 250 Hz for ordinary gypsum-board partitions. At this frequency the two panels vibrate out of phase with large amplitude, so the TL drops well below the single-wall value, creating a dip. This is the single most important factor that controls low-frequency insulation.

Well above the MAM resonance (roughly 2·fMAM or higher) the double-wall TL adds the two single-wall masses plus an air-gap term and increases at the steep slope of +12 dB/octave. For two 15 kg/m² gypsum panels at 500 Hz, for example, the single-wall value is around 30 dB while the double wall reaches about 55 dB — a 25 dB gain. Near the MAM resonance, however, you actually lose 10 to 15 dB in a narrow dip, so designs that care about low-frequency noise must keep the gap wide enough to push fMAM down.

Flanking is the indirect transmission of sound around the double-wall path — through the studs, bolts, pipes, ceiling and floor that join the two leaves rigidly. The structural bridging slider models this; a value of 0.3 cuts the TL by roughly 9% and 0.5 by 15%. In practice professional installers use independent (staggered) studs, sound isolation clips and resilient channels to break the rigid coupling. Skip this step and a wall computed to deliver 55 dB will routinely measure only 40 dB on site.

Duct (muffler) transmission loss describes acoustic energy reflected at area discontinuities inside a pipe — it depends on geometric ratios such as (S₂/S₁). The double-wall TL handled by this tool is governed by the mass law: airborne sound vibrates a solid wall and re-radiates on the other side, controlled by the impedance mismatch between air and the panel. The former describes fluid piping and exhaust systems, the latter describes building partitions, windows, speaker enclosures and soundproof rooms. The same letters "TL" describe physically different mechanisms.

Real-World Applications

Double-glazed and secondary-glazed windows: Apartments along busy roads commonly add an inner window behind the existing sash. With 3–6 mm glass panes and a 50–100 mm cavity, the TL above 500 Hz improves by 15–20 dB compared to a single pane and traffic noise feels less than half as loud. However a 50 mm cavity places fMAM at 100–200 Hz, so low-frequency rumble is only modestly suppressed. High-end products combine PVC frames, double glazing, and gaps of 100 mm or more to drive fMAM below 80 Hz.

Soundproof rooms and recording studios: Top-tier studios use a "room within a room" construction — outer wall, 100–200 mm air gap, inner wall. Mechanically separating the two leaves with double studs or resilient clips and channels is non-negotiable for breaking flanking. Filling the cavity with 100 mm of glasswool damps the MAM dip by 5–8 dB. Leading rooms target STC 60–70.

Speaker enclosures and instrument cabinets: Sealed enclosures and bass-reflex cabinets use double-layer MDF, damping mats and cavity stuffing to keep internal sound from leaking and to reduce panel ring. Subwoofers push fMAM below the 20 Hz audible threshold by combining very thick MDF (30–40 mm) with a narrow internal cavity.

Floor and ceiling acoustic retrofits in apartments: To control footfall and lifestyle noise from upstairs, designers add a suspended ceiling under the existing concrete slab, leaving a 100–250 mm cavity filled with mineral wool. A common pitfall is "drumming" — the suspended ceiling can amplify low frequencies, which is the same MAM resonance in disguise. Heavy double-layer gypsum, generous absorber and vibration-isolation hangers are the proper fix.

Common Misconceptions and Pitfalls

The biggest pitfall is believing that doubling the surface mass doubles the insulation. From the mass law TL = 20·log10(mf) − 47.4, doubling m adds only +6 dB, which corresponds to halving the sound intensity — not "halving the sound". Worse, raising the mass also lowers fMAM slightly (∝ √(1/m)), so the low-frequency benefit is muted. If low frequencies matter, widening the air gap beats adding mass on a cost-per-decibel basis.

Next, assuming that "absorber raises insulation". Glasswool is an absorber: it shortens the reverberation time inside a room, but it does not by itself add a large amount to the wall's transmission loss. Dragging the "Cavity damping" slider from 0 to 100 % moves the absolute TL only by a few decibels in this tool. Its real role is to flatten the MAM dip and cavity resonances; the mass-law region is still set by panel mass and air gap. A thin wall stuffed with glasswool is still a thin wall.

Finally, trusting the predicted TL to match the measured TL. This tool assumes an infinite flat panel under the mass law and a MAM resonance, but a real wall also exhibits coincidence dips (when the panel bending wave matches the air wave), finite-size effects, leakage around joints, and — biggest of all — flanking. Laboratory tests usually come in 3–5 dB below theory, and field installations 10–15 dB below. Design with a "theory − 10 dB" or "measured STC + 5 dB margin" guideline for safety.

Double-Wall Sound Transmission Loss (TL) Simulator

Double-Wall Transmission Loss and the Mass-Air-Mass Resonance

Frequently Asked Questions

Real-World Applications

Common Misconceptions and Pitfalls

How to Use

Worked Example

Practical Notes