Validation of an optimization procedure to improve low frequency characteristics of rooms

A set of experiments was carried out to validate an optimization procedure based on finite element method (FEM). The idea of the procedure, fully presented in previous edition of this journal [Zhu X, Zhu Z, Cheng J. Using optimized surface modifications to improve low frequency response in a room. Appl Acoust 2004;65:841-60], is to produce an optimal geometry modification on the wall for improving low frequency sound uniformity in small rooms. Four experimental models were set up with a scale of 1:5. One was modified according to the optimized result and the others were treated with no optimization consideration. Measured frequency responses of four rooms were compared with numerical results calculated by FEM models. The transient responses in these rooms were also measured and analyzed. The agreements between calculation and measurement are satisfactory though the discrepancies due to the uncertainty of acoustic behavior of the room boundaries remain. The optimization procedure has been supported by the results that the optimized room produces the flattest frequency response and also the most smooth energy decay within the frequency range studied. The reductions of response fluctuation have reached 4.3 dB for prediction and 2.6 dB for measurement, respectively.     

Application of a finite-element model to low-frequency sound insulation in dwellings

The sound transmission between adjacent rooms has been modeled using a finite-element method. Predicted sound-level difference gave good agreement with experimental data using a full-scale and a quarter-scale model. Results show that the sound insulation characteristics of a party wall at low frequencies strongly depend on the modal characteristics of the sound field of both rooms and of the partition. The effect of three edge conditions of the separating wall on the sound-level difference at low frequencies was examined: simply supported, clamped, and a combination of clamped and simply supported. It is demonstrated that a clamped partition provides greater sound-level difference at low frequencies than a simply supported. It also is confirmed that the sound-pressure level difference is lower in equal room than in unequal room configurations.     

The effect of construction material, contents and room geometry on the sound field in dwellings at low frequencies

An experimentally validated finite element method is used to model the sound level in rooms at low frequencies. It is demonstrated that the dimensions of rectangular rooms strongly influence the sound pressure level difference. Additional factors were investigated which are not normally considered in the frequency range where diffuse sound field conditions can be assumed. Three effects were investigated: room damping due to wall vibrations, furniture, the effect of small deviations from simple rectangular shapes. It is confirmed by field measurements that the vibrations of masonry walls and floors introduce less damping than surfaces of lightweight construction. Assigning to the FE model a damping equivalent to a surface absorption of 0.02 reproduces the effect of walls of heavyweight construction. Damping equivalent to a surface absorption of 0.15 reproduces the effects of plastered timber-frame walls, floors and ceilings. The work was briefly extended to a room pair built with heavyweight and lightweight material of construction. The modification of the shape of the room frequency response highlights well the effect of material of construction. In-situ and laboratory measurements show that furniture has little effect on steady-state room response below 100 Hz. Modelling a wall recess smaller than 0.5 m improved the agreement between prediction and measurements but the assumption of a simple rectangular room remains appropriate.     

Parameters influencing low frequency impact sound transmission in dwellings

As sound and vibration fields in dwellings exhibit modal behaviour at frequencies below 200 Hz, a systematic investigation of measurement and prediction uncertainty associated with impact sound transmission at low frequencies must include the effects of: location of the impact, type of floor, edge conditions, floor and room dimensions, room absorption and position of the receiver. Experimentally validated analytical models, described in a companion paper, have been used in an extensive investigation of impact sound transmission through rectangular homogeneous concrete floors and floating floors. The models were used to describe the effect of modal coupling and then to perform parametric and statistical studies aimed to identify the main factors affecting low frequency impact sound transmission.     

Using optimized wall section to improve low frequency response in a room

Three different wall sections with step shape were applied in the finite element analysis models set up to investigate the effect on low frequency sound field by wall modification. The heights of the step in three cases are taken as equal, random and optimized. The optimized value is obtained by using an optimization process with an objective function of minimum fluctuation in sound field. The frequency responses of rooms with original and modified walls were calculated in a range from 60 Hz to 120 Hz. The results showed that the room with an optimized wall section had the flattest frequency response. Same thing was true as the ratio of the room was changed. The largest improvement on fluctuation reached 4.5 dB. In addition, wall section with semicircle and triangle were studied. The rooms that wall section had optimized radius and heights also gave a better performance than those that had fixed radius and heights. Therefore, it is possible to use optimized wall section to improve low frequency sound field.     

Sound radiation from an aperture in a rectangular enclosure under low modal conditions

This paper investigates both theoretically and experimentally the sound radiation from an aperture placed in an enclosure wall for the particular case of low modal sound field. The incidence field is composed of the enclosed sound field, which is calculated using the theoretical modal model presented. The transmitted sound is calculated by the Rayleigh radiation equation after continuity conditions have been applied in the aperture plane, assuming the condition of a thin wall. The model is experimentally validated by measuring the directivity and sound pressure radiated from an aperture in the side of a rectangular box. Because the walls of the enclosure are not rigid, an experimental procedure to determine its admittance is also presented. The experiments have been carried out for the first four modes of the enclosed sound field, and good agreement is found between the theoretical and experimental results. These results indicate that the admittance of the aperture, its radiation efficiency, and its directivity are all functions of the predominant mode shape, and the frequency, as well as the location and shape, of the aperture relative to the predominant enclosed mode shape.     

矩形封闭声腔壁板轻量化对声固耦合特性的影响

基于模态耦合法建立了考虑对侧柔性壁板的矩形封闭腔体声固耦合模型,导出了耦合系统声振响应随柔性板材料属性及厚度变化的近似关系.通过数值仿真计算,详细分析了单柔性板-单侧激励、双柔性板-双侧激励及双柔性板-单侧激励三种情况下板的轻量化设计对系统声固耦合特性及腔内声压响应的影响.结果表明:对于单柔性板-单侧激励及双柔性板-双侧激励情况,低频段腔内声压主要取决于板厚,其次是杨氏模量,而与板密度关系较弱.因此使用适当增厚的轻质板可以同时达到减重和低频区降噪的目标.对于双柔性板-单侧激励情况,适当的轻量化设计可以显著增强两板间低频段振动的耦合,从而降低该频段的声腔模态响应及腔内噪音.在中高频段,增加板厚和材料密度对降低三种情况的腔内声压均有利。      

A hybrid finite element – statistical energy analysis approach to robust sound transmission modeling

When considering the sound transmission through a wall in between two rooms, in an important part of the audio frequency range, the local response of the rooms is highly sensitive to uncertainty in spatial variations in geometry, material properties and boundary conditions, which have a wave scattering effect, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency range, a computationally efficient modeling strategy is adopted that accounts for this uncertainty. The partitioning wall is modeled deterministically, e.g. with finite elements. The rooms are modeled in a very efficient, nonparametric stochastic way, as in statistical energy analysis. All components are coupled by means of a rigorous power balance. This hybrid strategy is extended so that the mean and variance of the sound transmission loss can be computed as well as the transition frequency that loosely marks the boundary between low- and high-frequency behavior of a vibro-acoustic component. The method is first validated in a simulation study, and then applied for predicting the airborne sound insulation of a series of partition walls of increasing complexity: a thin plastic plate, a wall consisting of gypsum blocks, a thicker masonry wall and a double glazing. It is found that the uncertainty caused by random scattering is important except at very high frequencies, where the modal overlap of the rooms is very high. The results are compared with laboratory measurements, and both are found to agree within the prediction uncertainty in the considered frequency range.     

Enhancing low frequency sound transmission measurements using a synthesis method

The characterization of low frequency sound transmission between two rooms via a flexible panel is investigated experimentally in this work. Previously, the individual effects of the transmission suite on the measured sound reduction index have been studied analytically, and the results have been compared with the ideal case of having free field radiation conditions on both sides of the panel. A new approach is proposed using a near-field array of loudspeakers driven by a set of optimized signals such that a diffuse pressure field is reproduced on the surface of the partition to be tested. The practical effectiveness of this method is assessed when using a set of 16 acoustic sources located in the source reverberant room in close proximity to an aluminium panel. The experimental results obtained confirm the dependence of the characterized sound reduction index on the particular test chamber considered in the low frequency range. They also validate the proposed synthesis method for providing an estimate that only depends on the properties of the partition itself.     

Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances

Two numerical procedures for finding the acoustic eigenvalues in the rectangular room with arbitrary (uniform) wall impedances are developed. One numerical procedure applies Newton's method. Here, starting with soft walls, the eigenvalues are found by increasing the impedances of each wall pair in small increments up to the terminal impedances. Another procedure poses the eigenvalue problem as one of homotopic continuation from a non-physical reference configuration in which all eigenvalues are known and obvious. The continuation is performed by the numerical integration of two differential equations. The latter procedure was found to be faster and finds all possible solutions. The set of eigenvalues allowed the room modal natural frequencies and damping constants to be obtained. From sound decays measured in a hard-walled rectangular room, and from the collective-modal-decay curve, the impedances of the hard walls are estimated. These are then used to find the reverberation times of the modes in the room with the floor lined with sound absorbing material of known acoustic impedance. It was found that a single reverberation time, for all modes, is only supported in the rectangular room with hard walls and at the higher frequency bands, consistent with Sabine's theory, which assumes a diffuse sound field. In the rectangular room with hard walls and at the lower frequency bands, and in the rectangular room with the floor lined with sound absorbing material and for all frequency bands, modes with rather distinctive reverberation times may produce sound decays not always consistent with Sabine's prediction.     

Effect of diffusive and nondiffusive surfaces combinations on sound diffusion

One of room acoustic goals, especially in small to medium rooms, is sound diffusion in low frequencies, which have been the subject of lots of researches. Sound diffusion is a very important consideration in acoustics because it minimizes the coherent reflections that cause problems. It also tends to make an enclosed space sound larger than it is. Diffusion is an excellent alternative or complement to sound absorption in acoustic treatment because it doesn’t really remove much energy, which means it can be used to effectively reduce reflections while still leaving an ambient or live sounding space. Distribution of diffusive and nondiffusive surfaces on room walls affect sound diffusion in room, but the amount, combination, and location of these surfaces are still the matter of question. This paper investigates effects of these issues on room acoustic frequency response in different parts of the room with different source-receiver locations. Room acoustic model based on wave method is used (implemented) which is very accurate and convenient for low frequencies in such rooms. Different distributions of acoustic surfaces on room walls have been introduced to the model and room frequency response results are calculated. For the purpose of comparison, some measurements results are presented. Finally for more smooth frequency response in small and medium rooms, some suggestions are made.     

Analytical and numerical study of acoustic intensity field in irregularly shaped room

The modal expansion method has been used to formulate expressions for real and imaginary parts of the complex sound intensity inside enclosures. Based on theoretical results, the computer program has been developed to simulate the acoustic intensity vector field inside the irregular room whose shape resembles the capital letter L. Calculation results have shown that a low-frequency distribution of the acoustic intensity is strongly influenced by the modal localization and the characteristic objects in the active intensity field are energy vortices and saddle points positioned irregularly inside the room. It was found that for small sound damping the vortex centers lie exactly on the lines corresponding to zeros of the eigenfunction for a dominant mode. An increase in a sound attenuation results in the change of vortex positions and can cause the formation of new vortices. Finally, an influence of the wall impedance on the quantitative relation between the acoustic and reactive intensities was studied and it was concluded that for very small sound damping the behavior of the sound intensity is basically only oscillatory.     

Performance Evaluation and Effectiveness of the Reverberation Room

This research presents a thorough evaluation of the reverberation room at Acoustics Laboratory in National Institute of Standards (NIS) according to the related international standards. The evaluation aims at examining the room performance and exploring its effectiveness in the frequency range from 125 Hz to 10000 Hz according to the international standard requirements. The room, which was designed and built several years ago, is an irregular rectangular shape free from diffusers. Its volume is about 158.84 m³, which meets the requirement of the ISO 354 standard L_max < 1.9V^1/3. Cut-off frequencies of one and one-third octave are 63 Hz and 100 Hz respectively; however Schroder frequency is 400 Hz. Calculations of cut-off frequency and modal density showed adequate modes that give acceptable uniformity starting comfortably from frequency of 125 Hz. The room has a reverberation time that is suitable for its size over the frequency range of interest. The room sound absorption surface area and its sound absorption coefficient satisfy the criteria given in ISO 3741 and ISO 354. There is an accepted diffuse sound field inside the room due to the standard deviation of measured sound level, which is less than 1.5 dB over all the frequency range. The only exception was 125 Hz which may be due to a lack of diffusivity of the sound field at this frequency. The evaluation proves that the NIS reverberation room is in full agreement with the international standards, which in turns qualifies the room to host measurements inside without concerns.     

Higher mode sound transmission from a point source through a rectangular aperture

This paper considers the higher-order scattered and transmitted wave fields that result when an acoustic wave from a point source impinges at an arbitrary angle on a rectangular aperture in a rigid, thick wall. In this analysis, it is assumed that free field conditions exist on both sides of the aperture. Although the full scattered and transmitted pressure fields contain both modal sum and modal coupling effects, the modal coupling effects of the higher-order modes are ignored such that an approximate analytical solution to the uncoupled analysis can be utilized. Experiments have been undertaken to measure the sound pressure levels in the transmitted field that result when sound from a point source impinges on the opposite side of a rectangular aperture. Measurements were made with the source located at the required position to drive a particular in-aperture higher-order mode. The source was also located at positions that did not directly excite any in-aperture higher-order mode at a cut-on frequency. These results indicate that the approximate analysis developed here gives accurate solutions whether or not any mode of the aperture is driven at cut-on. Thus, the method can be used for any relative location of a source from a rectangular aperture of any dimensions.     

Indirect measurement of acoustic power into a small room at low frequencies

An essential step towards improving sound insulation is a reliable means of quantifying the performance. However, for various reasons sound insulation measurements at low frequencies are associated with relatively high uncertainty and wide variance values. The objective of this research is to develop a method of sound insulation measurement which complements the standard ISO 140 measurement methods by providing improved accuracy at low frequencies. In this paper part of the problem is considered, namely the measurement of power radiated into the receiver room. The ‘peak envelope method’ is based on mode theory and the measurement employs a pair of microphones in the receiver room and a calibrated volume velocity source. No reverberation time measurements are required. The theory is outlined and computer simulations and trial measurements are carried out in order to validate the theory. Good agreement in numerical and experimental validation is demonstrated. We conclude that the peak envelope method is suitable for the measurement of radiated sound power at modal frequencies where ISO 140 methods are poorly adapted. In order to obtain transmission loss, a measure of incident power in the source room will also be required, which will be the subject of future works.     

基于声粒子分布积分的无网格声场计算方法

小尺度封闭空间内部声场的数值计算是声学设计、噪声控制等领域的关键技术。由于波动声学及几何声学方法计算频率上的限制,中频段声场计算问题一直是个难点。本文以声学无网格法为基础,提出了一种基于声粒子分布积分的无网格声场数值计算方法。文中利用声线跟踪理论计算声场中的声粒子分布,并以某个时间点上的声粒子作为蒙特卡罗法中的积分点,将其应用于无网格法中,从而获得声场中的节点声压。利用该方法对一个矩形封闭空间的中低频声场进行了计算,并与模态叠加法、商用声场计算软件、经典无网格法的结果进行了对比,证明基于声粒子分布积分的无网格声场数值计算方法在中低频段相较于传统基于网格的方法具有更高的精度。     

Monotonic curvature of low frequency decay records in reverberation chambers

In the papers by Larsen [1] and Brüel [2], two interesting problems connected with reverberation room measurements are pointed out and discussed. The first problem is that the ensemble averaged decay curve reveals a monotonic curvature at low frequencies. The second phenomenon is that often systematically larger sound power output values are reported at low frequencies according to the free field method than according to the reverberation room method. In searching for an explanation of these anomalies some measurements and a classical normal mode theory analysis have been made. It is shown that it is not possible to explain fully the curvature of the low frequency decay curves by means of the normal mode theory. The measured curves are more bent than the respective theoretical ones. Most probably, it should be possible to explain this lack of agreement by the fact that the absorption characteristics of normal reverberation chambers significantly deviate from the situation of uniform wall admittance which has been assumed in the theoretical deductions. The theoretical analysis and the comparison between theory and practice indicate that the damping characteristics of the individual waves vary much more than is predicted for a uniform wall admittance. This reasoning is supported by the observation that the monotonic curvature increases when a plane concentrated absorbent is added to one of the walls. One way to decrease the curvature has also been identified. When the room surfaces are provided with randomly placed small samples of low frequency absorbents the resulting decay curves turn out to be almost perfectly linear. Furthermore, it is found that the normal mode theory does not imply significantly different sound power output values than the ISO 3741 model. This fact has been verified with a comparative test. According to the normal mode theory the average sound power output as measured in the reverberant room should equal the free field output. Therefore, one is forced to conclude that the analysis of the classical normal mode theory fails in explaining the anomalies observed.     

Smart panel with active damping units. Implementation of decentralized control

This paper contains the second part of a study on a smart panel with five decentralized velocity feedback control units using proof mass electrodynamic actuators [Gonzalez Diaz et al., J. Acoust. Soc. Am. 124, 886 (2008)]. The implementation of five decentralized control loops is analyzed, both theoretically and experimentally. The stability properties of the five decentralized control units have been assessed with the generalized Nyquist criterion by plotting the loci of the eigenvalues of the fully populated matrix of frequency response functions between the five error signals and five input signals to the amplifiers driving the actuators. The control performance properties have been assessed in terms of the spatially averaged response of the panel measured with a scanning laser vibrometer and the total sound power radiated measured in an anechoic room. The two analyses have shown that reductions of up to 10 dB in both vibration response and sound radiation are measured at low audio frequencies, below about 250 Hz.     

Reverberation time measurements in non-diffuse acoustic field by the modal reverberation time

The increasing presence of low frequency sources and the lack of acoustic standard measurement procedures make the extension of reverberation time measurements to frequencies below 100 Hz necessary. In typical ordinary rooms with volumes between 30 m³ and 200 m³ the sound field is non-diffuse at such low frequencies, entailing inhomogeneities in space and frequency domains. Presence of standing waves is also the main cause of bad quality of listening in terms of clarity and rumble effects. Since standard measurements according to ISO 3382 fail to achieve accurate and precise values in third octave bands due to non-linear decays caused by room modes, a new approach based on reverberation time measurements of single resonant frequencies (the modal reverberation time) has been introduced. From background theory, due to the intrinsic relation between modal decays and half bandwidth of resonant frequencies, two measurement methods have been proposed together with proper measurement procedures: a direct method based on interrupted source signal method, and an indirect method based on half bandwidth measurements. With microphones placed at corners of rectangular rooms in order to detect all modes and maximize SNRs, different source signals were tested. Anti-resonant sine waves and sweep signal turned out to be the most suitable for direct and indirect measurement methods respectively. From spatial measurements in an empty rectangular test room, comparison between direct and indirect methods showed good and significant agreements. This is the first experimental validation of the relation between resonant half bandwidth and modal reverberation time. Furthermore, comparisons between means and standard deviations of modal reverberation times and standard reverberation times in third octave bands confirm the inadequacy of standard procedure to get accurate and precise values at low frequencies with respect to the modal approach. Modal reverberation time measurements applied to furnished ordinary rooms confirm previous results in the limit of modal sound field: for highly damped modes due to furniture or acoustic treatment, the indirect method is not applicable due to strong suppression of modes and the consequent deviation of the acoustic field from a non-diffuse condition to a damped modal condition, while standard reverberation times align with direct method values. In the future, further investigations will be necessary in different rooms to improve uncertainty evaluation.