Absorption keeps a room from ringing. Transmission loss is the other job entirely: keeping sound from crossing into the next space. The two are confused daily, and a submittal quoting an NRC where a TL was wanted has cost more than one project a rebuild.

The definition: $TL = 10\log_{10}\!\left(\dfrac{I_i}{I_t}\right)$, where $I_i$ is the sound intensity striking the partition in W/m² and $I_t$ the intensity radiated on the far side. A 40 dB partition passes one ten-thousandth of the energy that hits it — and is still perfectly audible from a loud room.

Where no test exists, the mass law predicts: $TL = 20\log_{10}\!\left(\dfrac{\pi m f}{\rho_0 c}\right) - 5$, read as TL equals twenty log of pi m f over rho-nought c, minus five. $m$ is the surface density in kg per square metre of face — mass per unit area, not total mass; $f$ is the octave band centre frequency in hertz; and $\rho_0 c$ — rho-nought-c — is the characteristic impedance of air, 415 rayls, the thing the panel is being compared against. The trailing $-5$ is the field-incidence allowance: laboratory sound arrives from every angle at once, and the grazing rays get through more easily than the head-on ones.

Read the shape and the economics fall out. Doubling the mass buys 6 dB. Doubling the frequency buys 6 dB. That means low frequencies are brutal — 40 dB at 125 Hz needs about 188 kg/m², which is 80 mm of solid concrete for one figure in one band. Nobody buys bass isolation with mass; they buy it with double leaves and a cavity.

And now the number that runs this lesson. Put a door in the wall and the ratings do not average — they combine in energy: $TL_c = 10\log_{10}\!\left(\dfrac{S_w + S_d}{S_w\,10^{-TL_w/10} + S_d\,10^{-TL_d/10}}\right)$. Here $S_w$ and $TL_w$ are the area and rating of the solid wall, $S_d$ and $TL_d$ the area and rating of the weak element — door, window, or an unsealed gap — and $10^{-TL/10}$ is that element's transmission coefficient $\tau$, the plain fraction of energy it lets through. Area-weight the $\tau$ values, then take one logarithm at the end.

Work it once and you will never forget it. An 18 m² wall at 45 dB with a 2 m² door at 20 dB: the assembly is 29.9 dB. Ten per cent of the area is carrying ninety-seven per cent of the sound. Upgrading that wall to 55 dB would move the assembly by about a tenth of a decibel. Fix the doors, the seals and the penetrations first — every time, on every job.