Predicted and Measured Low Frequency Response of Small Rooms

Abstract

The sound level difference of party walls at low frequencies [25–200 Hz] has been shown to be strongly dependent on the modal characteristics of the sound fields of the separated rooms. The modal characteristics can be modelled by numerical methods and a Finite Element Method has been selected to model sound transmission between adjacent rooms separated by a party wall. The numerical eigenfrequencies were compared with the theoretical eigenfrequencies to select a mesh model for which the eigenfrequencies are processed within an acceptable error range. As a prelude to the study of sound transmission between dwellings, the simulation of one single room, modelled with the selected mesh model, was validated by predicting the frequency response and comparing values with measured frequency response of a 1:4 scale room model. Results show promising agreement and establish the reliability of the work.

Sound Absorption at Low Frequencies: Modelling a Test Room

“…The average room temperature was measured as 20ºC, yielding a value of c 0 = 343 m/s. This small difference in sound velocity in air yielded significant shifts in the predicted room modes, since according to equation (5), the room eigenfrequencies are directly proportional to c 0 . As a result of these adjustments, it was possible to obtain an improved agreement between measured and predicted room frequency responses, as shown in Figure 11.…”

“…For rectangular rooms with hard surfaces, the general solution for the sound pressure inside an enclosure with dimensions L x , L y , and L z is: (4) where P 0 is the maximum pressure amplitude. The room response will be governed by frequencies given by: (5) Equations (4) and (5) specify, respectively, the shapes and natural frequencies of the acoustic modes that can exist in a rectangular room. If the cosine terms are expressed as exponentials, then equation 4can be written as: (6) where D is a constant, to be determined by the boundary conditions of a particular case.…”

“…In order to verify the accuracy of the rectangular empty room model, the room eigenfrequencies also were obtained analytically, according to equation (5). To evaluate the inaccuracy due to FE discretisation, an error E was calculated [9]: (12) where NE and AE are the numerical eigenfrequency and analytical eigenfrequency, respectively.…”

“…Unfortunately, it is at such low frequencies that simple theories of room acoustics and the relationships between sound level difference and sound reduction index are most tenuous. Current standards deal with frequencies more than 100 Hz, and despite the introduction of an annex (F in ISO 140/3 [2]), for sound insulation measurements at low frequencies, there is still a poor repeatability between measurement results [5]. The correction for receiver room absorption (and wall area), which relates the transmission loss of the separating wall to the sound level difference between the rooms, assumes a diffuse sound field condition.…”

Airborne Sound Level Difference between Dwellings at Low Frequencies

“…4x4x2.5m and 3.5x4x2.5m, the difference between FEM predicted eigenfrequencies and values obtained from equation 8was less than 10% for a 8-mesh model i.e. 8 3 elements [28]. For a brick party wall, the error was less than 10% for a 11-mesh model i.e.…”