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This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

# Calculations data: walls and air gap parameters#

The first wall | ||

The material from which the wall is made | ||

The density of the wall material | ||

Wall thickness | ||

The second wall | ||

The material from which the wall is made | ||

The density of the wall material | ||

Wall thickness | ||

Other | ||

Cavity width |

# Transmission loss at various frequencies#

Frequency [Hz] | Transmission loss [dB] |

31.25 | 44.54 |

62.5 | 50.56 |

125 | 56.58 |

250 | 62.6 |

500 | 68.62 |

1000 | 74.64 |

2000 | 80.66 |

4000 | 86.68 |

8000 | 92.7 |

16000 | 98.72 |

# 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 acoustic insulation of a single wall is limited by its
**thickness**and**density**of the material used. We can**overcome these limits**using**two walls**separated by**air gap**. The resulting system is called depending on the source:

- wall-air-wall,

- mass-air-mass,

- mass-spring-mass (more often found in theoretical papers where such a system is modeled by two masses connected with a spring).

- wall-air-wall,
**Sound reduction index**for**double wall**can be estimated using formulas introduced by London in 1950, updated later by Sharp in 1973:

$R(f) = \begin{cases} 20 ~ log\left[f \cdot (h_1 ~ \rho_1 + h_2 ~ \rho_2) \right] - 47, & \text{when } f <f_0 \\ R_1 + R_2 + 20 ~ log(f ~ d) - 29, & \text{when } f_0 <f <f_l \\ R_1 + R_2 + 6 & \text{when } f > f_l \end{cases}$where:

**$R$**- decrease of the sound intensity level of a partition consisting of two walls in decibels,

**$R_1, R_2$**- sound level decrease calculated for the first and second walls separately,

**$h_1, h_2$**- thickness of the first and second walls,

**$\rho_1, \rho_2$**- material density of which the first and second walls are made,

**$d$**- distance between walls (cavity width),

**$f$**- frequency of the acoustic wave,

**$f_0$**- resonant frequency $f_0 = \sqrt{\frac{\rho_0 \cdot c_0^2}{d} \cdot \frac{h_1 ~ \rho_1 + h_2 ~ \rho_2} {h_1 ~ \rho_1 ~ h_2 ~ \rho_2}}$,

**$f_l$**- limit frequency $f_l \approx \sqrt{\frac{55}{d}}$,

**$c_0$**- speed of sound in the air,

**$\rho_0$**- air density

# See also#

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**.

# Room within the room#

- A room whose
**all walls**and**ceiling**are surrounded by an empty air gap (the room has no common walls with others except a common floor) is often called a**room-within-the-room**. - The disadvantage of this solution is
**high cost**and**permanent modification of the building**. - For example, in order to isolate a medium-sized live room with a usable area of approx. 26 m
^{2}we need an additional approx. 24 m^{2}of empty space for air-gap insulation (assuming a distance between the walls of 1 m). Additionally, it is necessary to raise the entire building or to give up part of the height of the separated room (to leave an empty space under the outer room ceiling). - For this reason, classic room-within-the-room solutions are used only in specialized buildings, which of purpose is
**permanently**related to the need of high acoustic insulation such as recording studios or sound laboratories.

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# Links to external sites (leaving Calculla?)#

- wikipedia: sound reduction index
- insul.co.nz: law of mass in practice: design of walls and floors for good sound insulation
- estudogeral.sib.uc.pt: sound transmission through single, double andtriple glazing
- app.box.com: relative dBs build-up metric
- diva-portal.org: sound transmission through double walls using statistical energy analysis