The two sixes
Mass law says the transmission loss of a single limp panel rises 6 dB for every doubling of surface density and 6 dB for every doubling of frequency. Both fall out of the same logarithm, which is why they are the same number for lead, for glass and for plasterboard. Nothing about the material enters except its weight per square foot.
Run the default leaf through it — 2.2 lb per square foot, field incidence, no dip near the band — and 500 Hz gives 27.1 dB. One octave up at 1000 Hz gives 33.1. Double the weight instead of the frequency and you get the same 33.1 at 500 Hz. That equivalence is the whole rule stated twice.
The practical reading is deflating. A second layer of the same board, bonded into the same leaf, is worth about six decibels. Six decibels is audible and worth having, but it is not "twice as good", and people who expected twice as good tend to conclude the product failed rather than that the arithmetic did what arithmetic does.
Where the rule breaks
Every real panel is stiff, not limp. At one particular frequency the bending wavelength in the panel matches the wavelength of the sound arriving along it, the panel starts moving in step with the wave instead of resisting it, and transmission loss collapses. That frequency is the critical or coincidence frequency, and it depends on stiffness and thickness rather than on weight — which is why a thicker sheet of the same material has a lower one, and why laminated and damped products are sold partly on flattening the dip rather than on adding mass.
The default figures put the critical frequency at 2500 Hz with an 8 dB dip a full octave wide either side. The band table shows what that does: 1000 Hz comes out at 33.1 dB, and 2000 Hz — which mass law says should be 39.1 — comes out at 33.7. An entire octave of climbing gets cancelled. Above the dip the curve recovers and 4000 Hz lands at 42.6.
The dip depth and the critical frequency belong to the material and come off the test report. The width is different: it is a shape imposed here so the notch can be drawn across octave bands, and a measured curve is not a triangle. If you have third octave data, read the real notch rather than this one.
Working backwards, and when to stop
Ask the page for 40 dB at 500 Hz from mass alone and it comes back wanting 9.71 lb per square foot — 4.41 times the leaf in the form. That is the number that ends a lot of arguments. Nobody hangs nine and a half pounds a square foot on a stud wall, and if the target genuinely is 40 dB the answer was never going to be more layers.
What beats mass law is a second leaf with an air gap, because two leaves and a spring between them stop behaving like mass and start behaving like a mass spring mass system. Above the resonance of that system the curve climbs far faster than 6 dB per doubling. At the resonance it is worse than a single leaf of the same total weight. That resonance is set by the two surface densities and the cavity depth, cavity insulation moves it and damps it, and any structural connection between the leaves — a stud touching both faces, a screw, a rigid duct — short circuits the whole arrangement. None of that is on this page, and none of it is in mass law.
What the number is not
It is not a rating. A rating is a measurement of a specific assembly in a laboratory, condensed from a curve to a single figure using a weighting aimed at speech. This is an expression for one sheet, in one band, at one weight. The two answer different questions and the second is much narrower than the first.
It is also not a field result. Field performance is measured. A wall built exactly to a tested detail underperforms the test whenever there is a penetration, an unsealed perimeter, or a path around it that the test never had — and in a real building there usually is. Where the outcome matters, the answer is an acoustical consultant and an instrument, and anything the code touches is the authority having jurisdiction rather than any calculator.
Questions people ask
How much does a second layer of board add?
If the two layers act as one leaf, doubling the surface density is worth about 6 dB by mass law and no more, whatever the material. That is what the page prints for a doubling. In practice the second layer is often installed with damping compound between the sheets and a fresh round of perimeter sealing, and those two things can be worth more than the mass is — but they are separate mechanisms, and the mass part of the job stops at six.
What is the critical frequency and where do I get it?
It is the frequency where bending waves in the panel travel at the same speed as sound in the air alongside it, so the panel couples efficiently to the wave and transmission loss falls. It is set by stiffness and thickness, not by weight. Get it from the test report or the material datasheet for that material at that thickness — thin stiff sheets such as glass and sheet metal put it right in the range that matters, and a thicker sheet of the same material has a lower one.
Why is my measured wall so far off the mass law figure?
Because a wall is not one limp sheet. A stud cavity with two faces is a mass spring mass system that beats mass law well above its resonance and loses to it at the resonance, studs bridging the faces short circuit the cavity, and any unsealed path bypasses the whole thing. Mass law is the floor for a single leaf. The assembly test report describes the wall.
Field incidence or normal incidence?
Normal incidence is sound arriving square on to the panel and it is the form the expression derives directly. Real sound arrives from every angle, which transmits more, so a deduction is carried to estimate the field incidence case — 5 dB is the figure normally used and it is the default in the form. It is a modelling choice you are making. Change it if the source you have in mind is closer to one case than the other.
Does this tell me whether the wall meets the rating I need?
No, and it cannot. It is an expression for one sheet in one band, not a rating and not a measurement. Ratings come from a test report for a whole assembly, field performance is measured with an instrument, and whether anything is adequate for a code requirement is decided by the authority having jurisdiction and not by a page on the internet.