Modal energy

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International Symposium on Room Acoustics

-Satellite Symposium of the 19th International Congress on Acoustics-

Seville, 10-12 September 2007

S. Rolón, A. Montoya & R. Pesse
Acoustic Research Center, Universidad deSantiago de Chile, Av. Ecuador 54, Santiago, Chile,,

Sound insulation fulfillments inspection on building constructions and industrial noise control is fundamental for the advances on noise environmental laws. The traditional pressure-based methods of measuring sound reduction indexes require reverberant rooms for their implementation, and the real behavior of these rooms at low frequencies is not exactlyas the diffuse field model assume. Therefore, there is tendency to overestimate the sound insulation of a partition on those frequencies. Transmission loss measurements on two different situations according to ISO 140-4 were done, and through a finite element method, the low-frequency modal behavior of the rooms was analyzed. Considering the receiver room modal density on sound transmission lossmeasurements increased the method’s precision by getting closer to a real diffuse field case. The results for each situation were verified using the sound intensity method according to ISO 15186-2, which due to its characteristics does not need this consideration.

In the case of small rooms, where the largest dimension is much less than the wave length of the lowest frequency of interest, thenumber of tangential and axial modes in relation to the oblique modes is greater than in large rooms. The modal density inside is:

modos / hz

Due to these conditions, the relationship between sound pressure and intensity is not as stated in the method described by ISO140-4 to obtain sound power through pressure measurement methods [4].

30 25 20 15 10 5 0 50 63 80 100 125 160 200 250 315 HzCaso 1 Caso 2


4π c0

Sλ Lλ 2 f V (1 + + ) 8V 32πV


, where the term correction.

f 4π c0


Figure 1: Modal density of both receiving rooms.

Vξ corr

ξ corr

is the improved Waterhouse

The total acoustic energy inside the room, considering the energy density D and Equation, is:

The modal density below 400 [Hz] was determined from eigenvaluesobtained by the Finite Elements Method (FEM), applied to each receiving room, and taking into account all of the objects and furniture that might have an influence on the sound energy distribution inside the room. Figure 1 show the modal density on each receiving room. The reduction index, now considering the third octave band modal density, was determined by:

The fact that in smallrooms the energy density is greater on wall boundaries than over the rest of the room is a direct consequence of the interference effect. This effect is even greater at low frequencies due to the presence of quite separate modes from each other. In general, in classical architectural acoustics, this effect is not considered because its values are negligible [1], [2], which is valid if we considerthe range of frequencies often used in architectural acoustics up until the seventies, but it is actually in such frequencies where the initial hypothesis of a flux of equal energy in all directions and positions is not fulfilled. This is a very important concern if we consider the fact that one of the most important characteristics of modern systems and industrial machinery developed during thelast two decades is their capacity to irradiate low frequency sound energy. In the last few years, researches on sound insulation agree on one thing: the divergence of values obtained by sound pressure methods and sound intensity methods over the low frequency zone. Although pressure methods suggested by present standards offer acceptable results at mid frequencies, they do not consider the...
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