Mass law calculator for single layer
Calculator finds out sound reduction in decibels (dB) for single layer wall with given density and thickness using so-called mass law equation.

# Beta version#

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
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# Transmission loss at various frequencies#

 Frequency [Hz] Transmission loss [dB] 31.25 -inf 62.5 -inf 125 -inf 250 -inf 500 -inf 1000 -inf 2000 -inf 4000 -inf 8000 -inf 16000 -inf

# Sound insulation#

• When a sound wave moves through the air meets a barrier in the form of a wall, part of the acoustic energy is reflected, part is absorbed inside the wall (converted to heat), and the another part is transmited out (on the other side of the wall). We can write it mathematically as follows:
$\alpha + \beta + \tau = 1$
where:
• $\alpha$ - absorption coefficient (determines the part of the energy that was absorbed inside the wall),
• $\beta$ - reflection coefficient (defines the part of the energy remaining in the first room),
• $\tau$ - transmission coefficient (defines the part of the energy that was emitted to the second room).
• The transmission coefficient can be used as a measure of the acoustic insulation, because it determines the sound intensity ratio on both sides of the wall:
$\tau = \frac{I_t}{I_0}$
where:
• $I_t$ - intensity of the wave on the other side of the wall (sound intensity level audible in the second room),
• $I_0$ - incident wave intensity (sound intensity level audible in the first room).
• In practice, the transmission factor is most often given in the logarithmic scale. In this way, we obtain a decrease in sound intensity given in decibels, so-called transmission loss:
$\Delta TL = -10 ~ log (\tau) = 10 ~ log \left(\frac{1}{\tau}\right)$

# Some facts#

• The transmission factor for a uniform single wall can be estimated using the expression:
$\tau \approx \left[1 + \left (\frac{2 \pi \cdot f \cdot h \cdot d}{3.6 ~ d_0 ~ c_0} \right)^2 \right]^{-1}$
where:
• $\tau$ - transmission coefficient (part of the energy that passed through the partition),
• $f$ - frequency of the acoustic wave,
• $h$ - partition thickness,
• $d$ - material density the partition is made of,
• $d_0$ - air density,
• $c_0$ - speed of sound in the air.
• If the above expression after applying logarithmic scale, neglecting add a one (the component on the right is much greater than one - the wall density is about 1000 times greater than that of air) and moving the constants out of the logarithm, we get the equation known in building acoustics as the law of mass:
$\Delta TL \approx 20 ~ log (f \cdot h \cdot d) - 47.3$
where:
• $\Delta TL$ - transmission loss in the logarithmic scale (decibels),
• f - frequency of the acoustic wave,
• h - wall thickness,
• d - material density the wall is made of.
• The law of mass allows to estimate acoustic insulation at the air-solid boundary. In practice, this means that the mass law in above form applies to the airborne insulation (e.g. loud music or screaming).

If you're interested in calculators related to acoustics, check out our other calculators:
• Sound intensity level (dB) - if you want to learn what is decibel and how the sound intensity level is measured,
• Sound velocity in materials - if you want to learn how the type of substance affects the speed of acoustic wave propagation,
• Acoustic impedance of substances - if you want to learn what is acoustic impedance and how it depends on the type of substance,
• Sound wave reflection - if you want to find out how an acoustic wave behaves when it encounters an obstacle in the form of media boundary,
• Mass law: single wall - if you're interested in building acoustics and would like to estimate the acoustic insulation of a single wall,
• Mass law: double wall - if you're interested in building acoustics and would like to estimate the acoustic insulation of a double wall with an air gap between the walls,
• Sound absorption coefficients - if you're interested in acoustic adaptation of room and you would like to learn how different materials absorb the acoustic wave,
• Noise propagation - if you want to learn how sound intensity level changes with distance from the source,
• Sound insulation countours - if you want to learn more about acoustic insulation assessment standards used over the world,
• Sound reduction index (SRI) - if you're searching for acoustic insulation of popular building materials expressed in the coefficient Rw,
• Sound transmission class (STC) - if you're searching for acoustic insulation of popular building materials expressed by the index STC.