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#

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Calculations data: density and wall dimensions#

The material from which the wall is made
The density of the wall material
Wall thickness

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).