What the Coincidence Dip Is and Why It Lands Where It Does

Why this matters

Every partition has one frequency region where it performs far worse than its weight suggests, and on the gypsum board and glass that most buildings are divided with, that region sits inside the speech range. It is not a defect and no better installation removes it. What makes it worth understanding is the direction it moves: making a panel thicker, which raises its weight and every instinct you have, drags this weakness DOWN toward the frequencies you were trying to block. A shop that upgrades a glazed partition to heavier glass and measures a worse result for speech privacy has not been sold a bad product. It has moved a dip into a band it needed.

The mechanism

Sound arriving at a panel at an angle does not push the whole panel at once. The wave fronts sweep across the surface, and the spacing between successive fronts measured ALONG the panel is longer than the wavelength in air, by an amount that depends on the angle.

        incoming wave fronts, arriving at an angle
          \      \      \      \      \
           \      \      \      \      \
            \      \      \      \      \
  ============================================ panel
   |<--- trace wavelength along the panel --->|

A panel also carries its own bending waves, with their own speed and their own wavelength at each frequency. When the trace wavelength of the arriving sound matches the panel's free bending wavelength, the sound drives the panel exactly in step with a motion the panel already wants to make. The panel radiates efficiently into the other side and transmission loss falls. That is coincidence.

Because the trace wavelength is always longer than the wavelength in air, and gets shorter as the angle approaches grazing, the lowest frequency at which any angle can produce a match is the frequency where the panel's bending wavelength equals the wavelength in air. That is the critical frequency, and it is the bottom of the range in which coincidence can happen at all. Below it, no angle produces a match and the panel is mass-controlled. At and above it, there is always some angle that matches, and in a real diffuse field there is always sound arriving at that angle.

Where it lands

For a homogeneous, isotropic thin plate in free bending, the critical frequency is proportional to the square of the speed of sound in air, divided by the product of the plate material's longitudinal wave speed and the plate thickness. Two directions come straight out of that, and both matter more than the constant does.

• At constant material, the critical frequency is inversely proportional to thickness. Double the thickness and the dip moves down an octave.
• At constant thickness, the critical frequency is inversely proportional to the material's longitudinal wave speed, which is a stiffness-to-density property. Stiff light materials put their dips low. Limp dense materials put them high.

Approximate critical frequencies, for orientation only. Take the real curve from the tested report for the actual assembly, because framing, lamination and edge conditions all move it.

Read the concrete rows against the steel row. Thin steel puts its weakness above almost everything a building cares about, which is one reason a light sheet-metal enclosure behaves so predictably. Heavy concrete puts its weakness at the bottom of the range, which is why the mass-law card refuses to predict a concrete wall at 250 Hz.

What does not move it

This is the useful half, because most of what gets tried against a coincidence dip acts on something else entirely.

Room absorption does not touch it. The dip is a property of the panel's transmission. Absorption added in the receiving room lowers the receiving level and therefore raises the measured level difference, but it raises every band together and changes nothing about the shape of the dip.

Sealing does not touch it. A gap is a broad, high-frequency-weighted loss. Sealing improves the whole top of the range including the dip band, and the dip is still there when you re-measure, just riding on a higher curve.

Adding a second identical layer barely moves it. Two layers of the same board screwed together are not one panel of double thickness. Depending on how rigidly they are coupled, the assembly behaves somewhere between two independent panels, whose dips are both at the single-layer frequency, and one thick panel, whose dip is an octave lower. Screwed layers sit near the first case and a rigidly bonded lamination near the second, so the honest answer for a specific build-up comes from its tested curve rather than from arithmetic.

More mass of the same material moves it the wrong way. This is the one that costs money. Mass raises the curve everywhere by about 6 dB per doubling of surface mass at constant frequency, which the mass-law card owns, and thickness simultaneously drags the dip down an octave per doubling. Whether you win depends entirely on where the dip lands relative to the content you care about.

Two things that do work. Damping shallows the dip without moving it, because the depth of a coincidence dip is set by the panel's internal loss: a viscoelastic interlayer or a constrained damping layer is aimed squarely at this and at nothing else. And using two DIFFERENT thicknesses in a two-leaf assembly puts the two dips at different frequencies instead of stacking them, so neither one is a weakness of the whole assembly.

Worked example: a glazed office partition

An open-plan office is divided by single 1/4 in (6 mm) glazing, and the complaint is speech privacy: conversations are intelligible through it. Band level differences between the two sides, unweighted, Leq over 5 minutes, fixed positions:

The 2 kHz band is 7 dB below both of its neighbours. That is a local minimum in a curve that is otherwise climbing, which is the signature of coincidence rather than of a leak or a flanking path, and it matches the 1,800 to 2,200 Hz range for 6 mm glass. It is also the worst possible place for it: consonants carry most of the information in speech and most of their energy sits in the 2 and 4 kHz region, so this partition is transparent to exactly the content that makes a conversation intelligible.

The proposal that would have made it worse. Upgrading to 3/8 in (9.5 mm) glass raises the surface mass from 15 to 23.75 kg/m2, a ratio of 1.58, so mass law predicts about 4 dB more across the mass-controlled region. But thickness and critical frequency are inversely proportional at constant material, so the dip moves from around 2,000 Hz down to around 1,300 Hz, into the 1 kHz octave band that currently holds the partition's best result. Trade a 7 dB hole at 2 kHz for a comparable hole at 1.3 kHz and add 4 dB elsewhere, and speech privacy is very unlikely to improve. This is the purchase the arithmetic exists to prevent.

The proposal that addresses the mechanism. Laminated glazing of similar total thickness with a viscoelastic interlayer attacks the depth of the dip rather than its position, because the interlayer raises the assembly's loss factor and a coincidence dip's depth is set by damping. The critical frequency stays near that of the individual plies rather than dropping to that of a single plate of the combined thickness.

The proposal that adds a second leaf. A two-leaf glazed assembly using 6 mm and 9.5 mm plies puts the two dips at roughly 2,000 and 1,300 Hz rather than stacking them. Before recommending it, the double-leaf card's rule has to be run against the actual build. Glass at 2,500 kg/m3 gives 15 and 23.75 kg/m2. In a sealed insulating unit with a 12 mm cavity, using the empty-cavity constant of 60 because a sealed glazing cavity cannot be filled with absorption, the mass-air-mass resonance is 60 multiplied by the square root of 38.75 divided by the product of 15, 23.75 and 0.012, which is about 181 Hz. Below that the unit performs like a single leaf of the combined mass and there is a dip near 181 Hz. For a speech-privacy problem that is acceptable, since nothing in the complaint lives below 250 Hz. Widen the cavity to a secondary glazing arrangement at about 50 mm and the same arithmetic gives about 89 Hz, which is better if the partition ever has to deal with low-frequency plant noise as well.

Whichever option is chosen, two constraints travel with it and neither is acoustic. Handling and cutting glass is a laceration hazard, so it is handled with cut-resistant gloves, eye protection and enough people for the pane's weight, and heavier glazing may exceed the existing frame's design load, which is a question for the glazier and, where the frame is structural, an engineer. And if the pane sits in a location the building code designates hazardous, such as beside a door or in a wet area, the replacement has to be safety glazing under the code in the edition your authority having jurisdiction has adopted and amended, that authority being a named role with power to interpret and enforce rather than whoever inspects.

Sibling-rule check. The 6 dB per doubling of surface mass figure is quoted at constant frequency, as its owning card states it. The thickness-to-critical-frequency direction is stated once and applied consistently, including in the concrete rows of the table and in the mass-law card. The double-leaf option is checked against the mass-air-mass relationship before it is recommended, with the empty-cavity constant used and the reason given, and the resulting resonance is reported rather than assumed acceptable. All level differences are named as level differences between two positions, not as transmission loss.

How to verify you got this right

Look for a local minimum, not a low value. A single band that sits below both of its neighbours in a curve that is otherwise rising is a resonance of some kind, and the two candidates in a partition are coincidence, which sits near the critical frequency for the panel material and thickness, and a mass-air-mass resonance, which sits far lower and only exists if there is a cavity. Compute both before choosing between them.

Then confirm the fix acted where you claimed. A damping treatment should shallow the dip and leave the rest of the curve close to where it was. If the whole curve moved up and the dip is unchanged in depth, you added mass rather than damping, whatever the product was called.

References

• ASTM E90, laboratory measurement of airborne sound transmission loss, in the edition stated on the report; the band-by-band curve is where a coincidence dip is visible and the single-number rating can hide it
• Glazing manufacturer data giving transmission loss per band for the specific make-up, including interlayer type and cavity dimension
• The building code as adopted and amended by your authority having jurisdiction, for safety glazing requirements in hazardous locations and for any structural check on heavier glazing
• See related: What the Mass Law Predicts and Where It Fails; Why a Double Wall Beats a Heavy Wall and When It Does Not; What an STC Rating Covers and What It Misses