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# Sound Reduction Index

## Definition

The sound reduction index is the acoustic characteristic of a wall or floor for sound reduction purposes. It is given the symbol R, and it is not dependent on the characteristics of the room and its envelope. It is determined through laboratory measurements (though under specific circumstances it can be computed with a limited accuracy). The measurement procedure is given in Section 3.3.2.

## Predictive Computation

Computation of the sound reduction index of a single wall can be carried out using a prediction model. The crudest of these models is known as mass law; as implied by its name, it relies on the mass per surface unit of the wall, noted m. The main term of this law is 20 log(mf), meaning that doubling the mass will result in a 6 dB gain. Also, doubling the frequency will result in a 6 dB increase. Such a model can be enhanced by introducing a stiffness term.

Computation of the sound reduction index of a multiple wall can also be carried out using a prediction model. The crudest of these models features a description of each layer as per above, plus terms pertaining to the propagation inside the gap (filled by either air or a material) and to the coupling between the layers. Also, doubling the frequency will typically result in a 12 dB increase for a double wall.

A good insight can be gained in [29], which considers a one-dimensional model of single or multiple walls.

It is also possible to perform this computation through dedicated prediction computer programs. Of course, the more powerful the program, the trickier it is for somebody not familiar with the physics of sound transmission.

As implied by its name, a model is only a representation of reality. One must always try to master it first through the modeling of a well-known case to find out how to tune it. More to the point, one may not expect the model to always give an accurate prediction, but one may assess the probable variation of the sound reduction index due to a change in composition or dimensions.

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