Calculation of the Acoustic Transmission Loss - AcouVApp IsolX

Introduction

AcouVApp IsolX is designed to calculate the acoustic transmission loss of single and double partitions analytically, based on the findings of various research studies and internal R&D efforts.

Acoustic Transmission Loss (TL) measures the effectiveness of a material or structure, like a wall or partition, in reducing the amount of sound energy transmitted through it. This metric is essential for designing soundproofing solutions in buildings, industrial spaces, and other environments where noise control is crucial.

The global formula of the acoustic transmission loss is :

with τ, the tranmssion coefficient, W_in, the incident acoustic power and W_out the acoustic power radiated on the other sides of the panel

The objective of AcouVApp IsolX is to propose a comprehensive model (or a combination of models) that consolidates existing knowledge on acoustic insulation calculation, thereby assisting acousticians in their daily practice and to offer an educationnal tools easily accessible.

The next sections provide a detailed description of the theoretical foundations underlying the models, along with comparisons between calculated results and experimental measurements. Where appropriate, a brief discussion of potential improvements to the models is included. Input data for the calculations are presented alongside the resulting curves and have been sourced from material databases or estimated based on measurements.

Readers are encouraged to compare their data with the provided calculations and to reach out for further discussion and insights.

It is important to note that this model forms part of a more extensive framework developed by Impulsion Acoustique for research and development purposes. For detailed calculations tailored to your specific products, do not hesitate to contact us.

Theory of the models used in the calculation of the transmission loss of single and double wall

Single Wall Model (SWM)

The acoustic performance of materials (thin and isotropic) depends on the frequency of the sound wave relative to the material's critical frequency (fc). The following zones highlight how sound behaves across different frequency ranges:

• Zone 1: Below the Critical Frequency

  In this zone, the mass law governs transmission loss. Materials with higher mass density and thickness provide better soundproofing.

  In the this frequency range, the transmission loss increases of 6dB by doubling the frequency. Doubling the mass follows tha same law (+6dB).

• Zone 2: Around the Critical Frequency

  In this transition zone, the damping factor and the critical frequency significantly influence transmission loss. Material properties, such as elasticity and internal friction, become critical in this range.

• Zone 3: Above the Critical Frequency

  For frequencies higher than 1.2fc, transmission loss increases by approximately 9dB per octave. This zone is dominated by the material's damping factor. Materials engineered with high damping properties, such as viscoelastic composites, are particularly effective in this range.

• Zone 4: Above the limit of the thin plate theory frequency

  For frequencies higher than 4 times the frequencie of the thin plate theory, dilatationnal in the thickness appears that reduces the transmission loss. In many building or transportation materials (thin materials with bending modes only), these frequencies appear outside the frequencies ranges of interest (more than 5000Hz). But for thick material like concrete or blocks, these frequencies could be around 2000-3000Hz.

In AcouVApp IsolX, mainly the models use different theory developed last decades:

• The acoustic insulation is calculated using the models developed by Davy [1] for frequencies below the critical frequency. This approach accounts for the finite dimensions of the panel, unlike models assuming infinite panels. For frequencies above the critical frequency, the method proposed by Sharp [2] is used. This combined strategy aligns with the findings of Kosala [3], who concluded that this combination offers one of the most accurate results when comparing calculations to measurements.

• The model proposes also the possibility to add more than one layer (Multilayer Model). In [4] from Mansilla, they proposed to calculate and equivalent model of the different layers to perform the calculations. This model is only valid for spot laminated multilayers (screws or spot of glue and not glued on the total surface.) This approach works well for material quite close in term of characteristics (with closed critical frequencies) but could have more uncertainties when using materials very different.

• In high frequency where the thin plate theory (resonance in the thickness), a limitation is calculated based on calculations from Hopkins [5]. Indeed, for thick materials (like concrete), a reduction of the sound transmission loss appears due to thickness resonances at a frequencies higher than 6 times the thin frequency limit.

The current implementation does not account for orthotropic materials (materials with varying stiffness in different directions), which is under development. Additionally, composite materials (e.g., laminated systems with two panels and a soft core) are not yet supported. Furthermore, the first mode of vibration is not included in the calculations.

Double Wall Model (DWM)

A double wall is composed on 2 single walls (or multilayers) separated by a cavity that can be with or without absorption (airbone path). These 2 walls are connected by structural links (structure borne path).

For the transmission loss of a double wall, different frequencies ranges are important as show on the pictures:

• Before the mass-air-mass resonance (f0), the mass is coupled

• At the resonance frequency f0, the transmission loss decreased as the resonance between the mass coupled air cavity that play the role of spring.

• After the resonance, the mass is discoupled and the transmission loss increased up to 18dB/oct.

• In the higher part of this region, the structural links and absorbing material has an important effect.

• In the case of thin plate, the transmission loss decreased due to the different critical frequencies and it’s modulated by the damping of the plates.

For the double wall model, different theories have been used as the transmission loss can divided in 2 parts : The airborne and structureborne path.

• For airborne path, models developped by Davy [6][1] are used. These models describe the airborne behaviour along all the frequencies range below the mass-air-mass resonance frequency (f0) to above the last crirical frequency (fc2). This model has been used in many studies from the author [7] and other [8]. In these papers, Davy proposes an approach by calculating the transmission loss separately in three zones :
  • Below the f0, where the panels behave like a single wall
  • Between f0 and below the critical frequencies taking into account or not also the absorbing material inside the cavity
  • At and above critical frequencies, this frequency range is dependant of the damping loss factor of the different panels

• For structure path, Davy’model [15] is used. Indeed, different studies has been done to evaluate the transmission loss due to the links and the compliance (inverse of the stiffness) of the links. In our models, we use the line and points models [15] to calculate the transmission from the links.
  The calculation integrates also the compliance (that is frequency dependent) of the studs based on the works of Davy and al [14 ]16]. The compliances are estimated from double wall measurements by substracting the airborne path from the total and inverting the studs transmission loss loss to evaluate the corresponding compliance. The compliance of the studs depends of the studs spacing, the studs thickness, the total mass and the depth of the studs. In the model (line and points), the links are considered as rigid (Cm=0).
  At the end, the 2 transmission coefficients (airborne + structureborne) are summed to have the final transmission loss values.
  

• Some remarks about the model :
  • As for the SWM, the multilayer approach is based on Lin [11] that also calculates an equivalent model. The limitation is the same than the SWM.
  • From Rindel [12], the damping loss factor is a combinaison of the internal damping, the border damping (the connexion of the wall with surrondings) and damping from the radiation
  • The mass-air-mass resonance takes into account the presence of absorption in the cavity (isothermal or adiabatic)
  • Currently the absorption in the cavity is set to maximum 1 with a frequency curve depending of the depth of the cavity ([3]). As proposed in [3], for an empty cavity, the absorption is not set to 0 but a constant value depending of the cavity depth is added. A next version will include the air resisitivty to calculate the absorption with the possibility to change the material inside the cavity (thickness and absorption)
  • The studs compliance proposed in the model is an average of all calculations done by with some uncertainties. Moreover, the compliance is calculated on a base of US studs that could be different from other countries. So when some correlations are done take it into account and do not to hesitate to change the input data.
  • Another important effect not in the model, it’s the case where links are very stiff. In this case, the mass-air-mass resonance could change due to the coupling with drum modes between 2 links. This phenomenon could appear with wood studs or thick steel studs. See [17]

Applications of Acoustic Transmission Loss

Understanding the transmission loss behavior of materials and systems is crucial for:

• Building Design: Ensuring walls, floors, and ceilings meet noise control standards in residential, commercial, and industrial spaces.
• Product Development: Designing materials with tailored acoustic properties for maximum sound insulation.
• Regulatory Compliance: Meeting industry noise reduction standards for health and safety.

Learn More about acoustic

For further insights into acoustic performance and soundproofing solutions, explore the module to calculate the critical frequency or browse our acoustic product database to have an overview of acoustic performances of real products.

Comparison between experimental and calculations results of the acoustic transmission loss

Single Wall

Concrete 200mm