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Scientific Reports volume 14, Article number: 30584 (2024 ) Cite this article oak acoustic wood wall panels
Lightweight double leaf walls have been extensively employed in assembly and large-space buildings. Due to the complex and varied stud configurations in double leaf walls, accurately and efficiently predicting the sound transmission loss (STL) of such structures poses a significant challenge. To support performance-based design workflows, this paper presents an analytical model based on sound transmission path decoupling, enabling architects to quickly predict the STL of commonly used lightweight double leaf wall types, including wooden, steel, and acoustical stud constructions. The paper systematically discusses the impact of different stud configurations on sound insulation performance and reveals the underlying mechanisms of sound bridge effects. Results show that the sound bridge effect arises from the structural sound transmission path introduced by various types of studs in the wall, and optimizing stud configurations is essential for decoupling the two leaves of the wall acoustically. Traditional wooden studs, considered as rigid frames, contribute more to the sound bridge effect compared to steel studs of the same structure. A promising approach involving acoustical studs with rubber sound isolation inserts is proposed, which achieves high-level sound insulation performance while offering significant spatial and construction efficiency advantages. This study provides valuable insights into advancing high-performance, lightweight building partitions and contributes to enhancing indoor soundscapes.
Double leaf wall structures are widely used in prefabricated buildings, hotels and open offices, etc. as a flexible space division partition with the advantages of lightweight and convenient construction1,2,3,4,5. The typical form consists of gypsum board or calcium silicate board as the leaves, and wood or steel as the studs. The leaves and studs are fixed together through self-tapping screws, mechanism bolts, or spot welding. The cavity is usually filled with porous sound-absorbing material such as mineral wool or fiberglass. The goals of lightweight design and sound insulation performance optimization are mutually constraining6,7. It is affected by multiple factors such as the thickness and size, the structural resonance, the real mounting conditions, as well as the construction practices. Meanwhile, due to the combined flexibility of leaves and studs, optimizing high-performance sound insulation without significantly increasing the wall’s weight and thickness presents both significant potential and challenges.
Generally speaking, stud construction is primarily based on the consideration of overall structural strength. However, different types of studs introduce structural sound transmission paths, known as the sound bridging effect8,9,10. When the structural sound transmission path and the airborne sound transmission path are coupled, the sound transmission loss (STL) is generally reduced, particularly in the frequency band higher than the bridge frequency. Díaz et al.11 investigated the sound transmission through a multilayer lightweight concrete hollow brick wall by finite element method (FEM) and experimental validation. Arjunan et al.12 introduced a 2-D harmonic acoustic FEM to predict the sound insulation of stud based double leaf walls. However, modeling in FEM is complex and computationally expensive, making it challenging to adapt for evaluating the STL in numerous cases.
Extensive research has been conducted on the prediction and evaluation of sound insulation performance of lightweight partition walls13,14,15,16,17,18. In the early stage, the analytical model of double leaf wall mainly focused on the physical mechanism of airborne sound transmission path, without considering the influence of stud. The classical model proposed by Beranek and Work19 and London20, only considered the case of the infinite double leaf wall under normal sound wave incidence and the cavity without porous material filling. Then, based on the Paris Theorem, Mulholland et al.21 extended the classical model to adapt to different sound wave incident angles and diffuse incident situations, which greatly improved the practicability of the classical model in dealing with real structures. Considering the size effect, Sewell22 introduced the concept of limiting angle, which is generally defined as 78°, to avoid the non-ideal diffuse incident sound field environment under experimental conditions. This hypothesis can effectively avoid the sharp decrease of sound insulation caused by acoustic grazing incidence and can make the simulation results closer to the experimental results near the critical frequency. Based on the study of Cremer and Heckl et al.23 about the admittance of plate structures under force excitation, Sharp24 proposed the widely accepted prediction model of double leaf walls that adopts the sound transmission path decoupling approach, in which the wooden stud is treated as an equivalent, completely rigid connector. Considering the experimental observation that the STL of double leaf walls with steel studs is higher than those with wooden studs, Gu and Wang25 reviewed the theoretical basis of Sharp’s model and introduced the parameter of studs’ transverse line stiffness. This parameter better captures the inconsistent velocities on the top and bottom sides of the steel stud due to its elastic deformation during vibration transmission. Wang et al.26 modeled the stud of the infinite double leaf wall as massless springs (including torsional and translational), and found that for common light steel stud, the torsional effect can be ignored, with transverse vibration transmission being the dominant factor. Based on the work of Sharp24, Gu and Wang25, Davy et al.27,28,29 proposed a more comprehensive prediction model in which the sound bridge effect is reduced to point connection or line connection. The outstanding contribution of this model lies in the introduction of a frequency-dependent parameter, denoted as the stud’s transverse compliance (the reciprocal of stiffness). Once the spectra of different types of studs are obtained, the sound bridge effect can be easily characterized, as demonstrated by his recent work on determining the transverse compliance of 20 gauge studs30. Meanwhile, the issue of sound transmission in composite laminated structures has attracted significant attention from researchers. Talebitooti and collaborators31,32 proposed efficient analytical models based on higher-order shear deformation theory, providing valuable insights for optimizing the performance of such structures. Comprehensive reviews are also available for further exploration of the sound insulation characteristics of composite laminated structures33,34.
To enhance the sound insulation performance of double leaf wall, it is essential to minimize the sound bridge effect by employing various techniques, such as incorporating the sound isolation clips, elastic damping pads, and other similar measures (Fig. 1)35,36,37. The challenge in predicting the STL of double leaf walls primarily stems from the mechanical connection caused by sound-vibration coupling. The advantage of experimental research lies in its focus on real structural samples, which, to a certain extent, minimizes the errors introduced by the assumptions and simplifications inherent in theoretical models. However, experimental research requires a significant amount of human and material resources and may not clearly reveal the underlying physical mechanisms. In the design and optimization stage, analytical models can be employed to quickly and clearly draw conclusions by defining explicit physical parameters. Existing research on lightweight partition walls faces two primary limitations. First, while the structural types of such walls are highly diverse, most studies focus on traditional wooden studs and certain steel stud varieties, lacking a systematic comparison of sound insulation performance across different stud types. In particular, research on innovative designs such as acoustical studs remains sparse. Second, from a methodological perspective, current studies tend to rely on numerical models, analytical methods, or experimental techniques in isolation. However, there is a lack of a practical sound insulation prediction framework designed specifically for building practitioners—rather than acoustics specialists—that is convenient to implement during the design phase. Thus, this study introduces a simple and efficient analytical prediction model, thoroughly investigates the impact of various stud types on the sound insulation performance of double leaf walls, and proposes a high-performance double leaf wall configuration based on acoustical studs. These findings provide new technical insights to advance the development of lightweight, high-performance building partition walls in building engineering.
The picture of stud construction practice to attenuate sound bridge effect. (a) Sound isolation clips type 1; (b) Sound isolation clips type 2; (c) Elastic damping pads.
The remainder of this paper is structured as follows: In Sect. “Theoretical methodology”, the theoretical methodology utilized in this paper is introduced. In Sect. “Validation of prediction model”, the accuracy of the methodology is verified with the experimental data in literature. Section “Results and discussion” compares the sound insulation characteristics of different double leaf wall cases with three types of studs, and discusses the parameters effect on sound transmission loss of the wall. Then, in Sect.“Experiment with an optimal configuration with the acoustical stud”, an optimal double leaf wall configuration with the acoustical stud is designed, and its airborne sound insulation performance is evaluated experimentally and analytically with the present approach. Finally, the conclusions are summarized in Sect. “Conclusions”.
The sound bridge effect means the introduction of mechanical connections by different stud types between two leaves of double wall structure to transfer vibration energy. To achieve the best sound insulation performance, the two leaves must be mechanically or acoustically isolated from each other as possible.
As shown in Fig. 2, when the sound transmission path is decoupled to consider the influence of sound bridge effect, it can be divided into airborne sound transmission path, and structural sound transmission path. The first is the sound radiation energy part (\(P_{2a}\) ) of the transmitted plate stimulated by the radiated sound wave of the incident plate entering the cavity, and the second is the part of sound energy transmitted directly through the studs (\(P_{2b}\) )38.
Diagram of the decoupling method in sound transmission analysis, where the wooden stud is considered as massless rigid connection and the steel stud is considered as massless spring with transverse compliance varying with frequency.
Wooden studs are generally considered as completely rigid, and the local velocities on both sides of the stud are equal. Steel studs with the thickness of 0.5 mm ~ 1.2 mm, whose flange will undergo elastic bending deformation in transverse vibration, can be considered as a translational spring with equivalent stiffness varying with frequency, and its local velocities on both sides are not equal. The acoustical studs further reduce the stiffness of the stud by introducing flexible rubber damping pads and are also considered as flexible connection.
The analytical models are based on the decoupling method, which extends Cremer and Heckl ‘s23 near field radiation formulas from a point or line force exciting plate. Due to the relatively small cross-sectional area and low mass fraction of studs in double leaf walls, they do not act as barriers to impede sound waves. Instead, their primary role is to connect the two leaves and increase the overall structural stiffness. Based on this, two key assumptions can be made to enhance the computational efficiency of the model without compromising the accuracy of the results: a) The studs only participate in the transmission of vibration energy, and its mass can be ignored; b) The studs have no sound vibration coupling with the medium in the cavity. The transmitted energy is calculated as the sum of the energy of two sound transmission paths. Thus, the STL of double leaf wall with different stud types can be expressed as
where \(P_{1}\) and \(STL_{a}\) are the radiated sound energy and the STL caused by the airborne sound transmission path, respectively. \(STL_{s}\) indicating the STL only the structural sound transmission path is considered, which can be expressed as the STL of the ideal double wall composed of leaf 1 and 2 (\(STL_{1 + 2}\) ) plus a correction term caused by different types of studs (\(\Delta STL\) ), which can be written as39
Sharp initially assumed that the studs were completely rigid and that the local velocities on both sides of the bridge were the same, i.e., \(v_{s,1} = v_{s,2}\) . Meanwhile, the relationship between the average speed on leaf 1 (\(v_{1}\) ) and the local speed at the bridge of leaf 2 (\(v_{s,2}\) ) can be expressed by the impedance generated by the point connection or line connection between the two panels (\(Z_{1} , Z_{2}\) )39
If the average velocity on panel 1 with the area S is approximately equal to the average velocity of the ideal double wall structure, and the radiation efficiency is approximately equal to 1, \(\Delta STL\) in Eq. (2) can be expressed as
Wooden studs, steel studs, and acoustical studs can all be equivalently modeled as either point connections or line connections, depending on the spacing between the studs. Point connections are applicable when the stud density is relatively high, typically around 300 mm. In contrast, line connections are used when the stud density is sparser, generally around 600 mm. The characteristics of a sound bridge can be determined by the mechanical impedance of the panel, and can be expressed as
where, \(F\) is the structural coupling force by which the sound bridge affects the plates. Steel studs and acoustical studs with different cross-sectional shapes can both be considered flexible studs. Therefore, the impedance of the plates is determined by the dynamic stiffness of the studs (\(k_{d}\) ). The dynamic stiffness quantifies the resistance of the studs to vibrational motion when subjected to dynamic forces. To calculate the variable, information regarding the stud’s mass and its response to dynamic loading is typically required, which is usually obtained through a frequency response analysis. In this study, the values derived by Davy et al.40 are adopted for the theoretical calculations.
For point excitation, the sound radiation energy of the panel excited by n points equally can be written as
Accordingly, the point impedance is
Substitute Eqs. (6), (7) into Eq. (4) yields
For line excitation, the impedance of the panel can be written as
where \(L_{\ell }\) is the length of line connection. Generally, studs are arranged periodically, allowing the length of the line connection to be determined by measuring the distance between adjacent studs and the fixed points on the wall leaves.
The sound radiation energy of the panel for line connection denotes
Substitute Eqs. (9), (10) into Eq. (4) yields
Figure 3 summarizes the STL variation trend of double leaf wall considering sound bridge effect41. There are three key frequency points: mass-spring-mass resonance frequency, bridge frequency, and coincidence frequency.
Diagram of the STL spectrum trend of the double-leaf wall with studs.
The mass-spring-mass resonance is related to the total weight of the leaves and the depth of the cavity. This frequency was initially discussed under the ideal circumstance of double wall structure, i.e., on normal incidence, no fill, no stud connection. This is done by assuming that the two panels are connected by an equivalent stiffness spring provided by the air gap.
The normal incident mass-spring-mass resonance frequency can be written as
Considering the coupling between structural resonance and stud connection, Davy et al.40 proposed the concept of effective resonance frequency to explain the phenomenon that the measured mass-spring-mass frequency is slightly higher than the normal incident resonance frequency.
(2) Limiting frequency and bridge frequency.
The limiting frequency is that the sound wave in the cavity impacts the panel directly forming standing wave, which refers to the lowest order cavity resonance frequency. The formula can be written as
According to the spacing of studs and screws, there are two ways of simplifying sound bridge, which is point connection and line connection. The structural coupling degree of point connection to the panel is lower than that of line connection under the same studs’ spacing condition, so the value of STL is higher. According to Nightingale et al.42, if the distance of point connection is less than half of the bending wavelength, it can be thought as line connection. With the increase of frequency, the behavior of point connection gradually begins to be different from that of line connection. Therefore, with the rise of frequency, it is transited from air transmission to structural transmission in a certain frequency range, which is defined as bridge frequency where the two paths transmit the same energy.
The coincidence frequency explains that when the forced bending wavelength matches the wavelength of the incident wave, where a significant decrease in sound insulation performance occurs. The lowest value of the frequency, also known as the critical frequency, occurs at grazing incidence. Real experimental conditions can be better simulated by controlling the limiting angle of incident sound waves. The critical frequency can be calculated as
where \(B\) and \(m\) are bending stiffness and surface mass of the panel, respectively.
The trend spectrum is divided into six segments based on the key frequency points. The change in each segment is summarized as follows41:
In the band (1): Below the mass-air-mass resonance frequency, the two leaves are coupled together to carry out in-phase motion at low frequency, behaving like a single-layer wall, and the STL is mainly determined by the mass law increasing with 6 dB/octave.
In Davy’s model, in the frequency band from \(f_{0}\) to \(2/3f_{0}\) , the STL is derived from the value of the endpoint by linear interpolation. In Sharp’s model, only this frequency is identified, and the change around the frequency cannot be calculated.
In the band (2): At frequencies where the wavelength is large compared to the depth of the cavity, i.e., \(kd \ll 1\) . the STL increases by 18 dB/ octave when the two sides of the plates are acoustically decoupled above the mass-air-mass resonance frequency (\(f_{0}\) ).
In the band (3): When the cavity width is equivalent to the incident wavelength at \(f_{l}\) , the cavity mode couples the two plates together, and the STL increases by 12 dB/octave. If the sound bridge effect exists, the STL above the mass law is constant and increases by only 6 dB/octave.
In the band (4) & (5): The sound insulation performance is caused by the coincidence effect. The STL increases by 12 dB/octave above the critical frequency (\(f_{c}\) ) in Sharp’s model.
The diffuse transmission coefficient can be obtained by integrating the transmission coefficient of all possible solid incident angles, which can be written as
Sewell22 developed the concept of limiting angle to explain the size effect of the structure on radiation efficiency. The limiting angle is approximately to be chosen as 78° ~ 85° to avoid the non-ideal diffuse incident sound field environment, which can give a good agreement with the experimental results.
In this section, the experimental data of a double leaf wall case with the C-type steel stud in Legault et al. ‘s paper10 is selected to verify the accuracy of the analytical model method presented in this paper. Figure 4 shows the construction diagram of the wall. The size of the sample is 1.2 m × 2.1 m. The leaves on both sides are made of aluminum with the thickness of 1 mm and 2 mm, respectively. The cavity has a depth of 50.8 mm and is filled with fibrous material. The C-type steel frame is also made of aluminum with a thickness of 3.175 mm and a spacing of 508 mm. Detailed material parameters can be found in Ref.10.
Section diagram of double-leaf wall configuration with the C-type steel stud.
Figure 5 presents the diffuse incident sound transmission loss spectrum of the double leaf wall. In order to more clearly compare the sound bridge effect caused by the insertion of the stud, the result of the same construction without the studs is also presented. On the whole, the analytical model based on the sound transmission path decoupling is in good agreement with the airborne sound insulation experimental data in reverberation chamber. Based on Eqs. (12) ~ (14), the mass-spring-mass resonance frequency, bridge frequency, and coincidence frequency for the structure are approximately 158 Hz, 452 Hz, and 6121 Hz, respectively. This shows the validity and accuracy of the model adopted in this paper. The inclusion of studs in double leaf walls is generally intended to connect the two leaves for strengthening the whole wall, which inevitably introduces the sound bridge effect. Specifically, in the frequency band above 452 Hz, the STL of the C-type steel wall with stud is significantly reduced. With the increase of frequency, the gap between the sound insulation performance of the two kinds of walls with and without studs increases rapidly, and the maximum can reach about 30dB. This indicates that the two leaves of the wall gradually couple acoustically as the frequency increases, resulting in an intensification of the sound transmission.
Comparison between the analytical results and experimental data from Legault et al.10 of the double-leaf wall configuration with the C-type steel stud.
In this section, the analytical model is employed to compare the sound insulation characteristics of double leaf walls with different configurations. Firstly, the construction and material parameters of 13 types of double-leaf walls composed of different forms of wooden, steel, and acoustical studs are presented in Sect. “Construction and material properties”. Subsequently, in Sect. “Sound insulation characteristics of double leaf wall with different stud configurations”, the influence of the sound bridging effect induced by different stud types on the sound transmission loss of the double leaf walls is analyzed. Finally, the parametric effects of stud spacing and wall dimensions on the sound insulation characteristics of the structures are discussed in Sect. “Parametric effects and discussion”.
As shown in Fig. 6, in the field of building engineering, the common stud forms of double leaf walls can be divided into three types, namely wooden, steel and acoustical studs. Among them, the wooden studs are usually considered to rigidly connect the two leaves together of the wall. The cross-section of wooden stud is 38 mm × 90 mm, and the linear density is 1.6 kg/m43. Steel studs have a variety of different forms, generally according to the section shape can be named as C-type, H-type, W-type, Z-type and O-type, etc. The conventional section thickness of steel stud is 0.5 mm ~ 2 mm. The acoustical stud is divided into three categories, namely staggered studs, double studs, and rubber isolation clips.
The section diagram of the three types of studs studied in this paper, as wooden studs, steel studs, and acoustical studs.
Table 1 lists the construction properties of 13 kinds of double leaf wall cases with different stud forms studied in this paper. These configurations have a consistent size of 3.05 m × 2.44 m. The stud spacing is uniformly set to 600 mm; therefore, unless otherwise specified, the line connection model is used. Gypsum board is used as the material of the leaves. The cavity is not filled or filled with the mineral fiber wool. The material parameters of the double leaf wall cases are shown in Table 2. During the measurement of sound insulation performance in practical engineering applications, the value of the loss factor is very sensitive to the fixation degree of the sample and the test frame. Therefore, the in-situ loss factor is used in the prediction model, which is the combination of the inner loss factor of the material and the support loss factor41.
In this section, a comparative analysis of the airborne sound insulation characteristics of 13 different double leaf wall configurations with various types of studs, as listed in Table 1, is conducted based on the model proposed in this paper.
Figure 7 presents a comparison of the sound transmission loss spectra for Cases A1 and A2. These two configurations have identical wooden studs, with the only difference being the number of layers of gypsum board used in the leaves. In the present model, wooden studs are considered rigid connections. It is also assumed that the multilayer laminated panels can slide relative to each other completely. When the thickness of the double-layer laminated plate is twice that of the single-layer plate, the Young’s modulus is one-fourth that of the single-layer plate. It can be observed that Cases A1 and A2 share the same mass-spring-mass resonance frequency and coincidence frequency within 1/3 octave bands of 125 Hz and 3150 Hz, respectively. Due to the influence of surface density, the STL of Case A2 is approximately 3 dB higher than that of Case A1 overall. Meanwhile, due to the action of the wooden studs, the coupling of the two leaves in sound transmission causes the bridge frequency to occur between 250 and 500 Hz. The rigid studs prevent the two configurations from achieving a single-number rating value greater than 45 dB44.
The 1/3 octave STL spectra of double-leaf wall cases with the wooden studs.
Figure 8 presents a comparative analysis of the sound transmission loss spectra for Cases B1 to B6. This set of configurations adopts different forms of light steel studs, such as C-type, H-type, W-type, Z-type, and O-type. In the analysis of sound transmission paths, light steel studs are considered flexible and can be modeled through a combination of springs and dampers. Due to different stud forms exhibiting varying stiffness, the impact of sound bridging effects on the structural sound insulation performance also differs. Specifically, Fig. 8(a) compares the influence of filled porous materials on the sound insulation performance of the wall. It can be observed that filled porous materials have a certain degree of improvement in the mid-to-high frequency range (125 ~ 4000 Hz), with a maximum enhancement of approximately 5 dB. Porous materials are typically lightweight and fluffy. The presence of pores increases the number of interfaces, enhancing the likelihood of sound wave reflection and refraction. As a result, more sound energy is absorbed by the material rather than transmitted through it. In the low-frequency range, the inertia of the porous material is relatively low, allowing it to move in sync with the particle velocity of the sound wave, resulting in weaker noise reduction performance. In the mid-to-high frequency range, the impedance mismatch between the material and air, coupled with friction and damping mechanisms, enhances the absorption and dissipation of sound energy41. This more effectively suppresses rapid sound wave vibrations and reduces the amount of sound transmitted through the material. Meanwhile, they have little effect on improving the structural sound insulation performance against the sound transmission dips caused by the mass-spring-mass resonance and coincidence effects. Figure 8(b) compares the influence of C-type steel studs’ thickness on the sound insulation performance of the wall. Among them, the cross-sectional thickness of studs for Cases B2 and B3 is 0.53 mm and 1.22 mm, respectively. It can be seen that the cross-sectional thickness of the studs has a significant impact on the airborne sound insulation performance of the double leaf walls in the frequency range above the bridging frequency (> 165 Hz). With the increase in the studs’ cross-sectional thickness, the lateral flexibility of the studs decreases correspondingly, leading to a more pronounced sound bridging effect. Figure 8(c) compares the sound insulation performance between different forms of light steel studs and wooden studs. It is evident that the overall sound insulation performance of the double leaf wall configuration with wooden studs (Case A1) is significantly lower than that of the four configurations with light steel studs. The bridging frequency induced by the insertion of light steel studs occurs between 250 and 500 Hz. Among these four configurations, Case B5 with W-type steel studs exhibits the optimal sound insulation performance, followed by Case B4 with C-type steel studs. This indicates that the sound bridging effect induced by these two types of steel studs is relatively weak. Therefore, in building engineering, W-type and C-type steel studs should be preferred to make the double leaf wall have superior airborne sound insulation performance.
The 1/3 octave STL spectra of double-leaf wall cases with the steel studs. (a) The influence of porous materials in the cavity; (b) The influence of the thickness of C-type steel studs; (c) The influence of the types of studs.
Figure 9(a) presents a comparative analysis of the sound transmission loss spectra for double leaf wall configurations with different forms of acoustical studs. Acoustical studs can be broadly categorized into two types: one involves the conventional arrangement of wooden or light steel studs in staggered or parallel configurations (Cases C1 ~ C4); the other employs rubber isolation clips added to light steel studs to decouple the two leaves of the wall in the sound transmission path, as exemplified by Case C5. It can be observed that Cases C2 ~ C5 show relatively similar airborne sound insulation performance, which is significantly higher than Case C1. It’s worth noting that the conventional staggered or parallel arrangement of studs generally results in thicker double leaf walls, while Case C5 achieves superior sound insulation performance while maintaining a thinner thickness. Specifically, the thickness of the double leaf wall with double C-type steel studs is 205 mm, while the thickness of Case C5 with rubber isolation acoustical studs is only 145 mm in this paper. Figure 9(b) compares the sound transmission loss spectra for Case A1 with wooden studs, Case B5 with W-type light steel studs, and Case C5 with acoustical studs. It can be seen that due to the wooden studs being considered completely rigid, Case A1 exhibits the worst sound insulation performance, while Cases B5 and C5 show relatively similar overall sound insulation performance. The main difference between Cases C5 and B5 is in the frequency range above the mass-spring-mass resonance frequency, where the sound insulation performance of Case C5 with acoustical studs is higher than that of Case B5 with light steel studs.
The 1/3 octave STL spectra of double-leaf wall cases with the acoustical studs. (a) The influence of the types of acoustical studs; (b) The comparison of the wooden stud, W-type steel studs and Rubber isolation acoustical studs.
The sound bridge effect originates from the structural sound transmission path created by the studs connecting the two leaves of the double leaf wall. It is essential to focus on designing stud configurations that decouple the two leaves acoustically. Overall, after the analysis of the three major categories of double leaf wall configurations with different stud forms, it is suggested that priority should be given to the selection of rubber isolation acoustical studs, W-type and C-type steel studs. The aim is to achieve the goal of improving airborne sound insulation performance while reducing the walls’ thickness and weight as much as possible.
To further investigate the influence of key parameters on the airborne sound insulation performance of double leaf wall configurations, this section takes Cases B5 and C5, which exhibit superior sound insulation performance, as examples. The effects of stud spacing and wall dimensions are explored to better provide data-driven guidance for the practical application of double leaf walls in engineering projects.
Figure 10 illustrates the influence of stud spacing ranging from 100 to 900 mm on the sound insulation performance of Case B5. It can be observed that the studs spacing can affect the airborne sound insulation performance across the entire frequency range of interest. A smaller stud spacing results in a higher mass-spring-mass resonance frequency, indicating a greater apparent bending stiffness of the structure. As the stud spacing increases, the resonance frequency of the double leaf wall gradually shifts to lower frequencies. Below the resonance frequency, the wall is in the stiffness-controlled region, where sound insulation performance improves as the stud spacing decreases.
The influence of stud space of the double-leaf wall cases with the W-type steel stud (Case B5).
Figure 11 presents the influence of studs spacing ranging from 100 to 900 mm on the airborne sound insulation performance of Case C5. It can be found that as the studs spacing increases, the sound insulation performance of this configuration gradually improves. However, there exists an interesting phenomenon that the variation in spacing of acoustical studs affects the sound insulation performance only in the frequency range above the bridging frequency (> 250 Hz), compared to Fig. 10. This is mainly due to the fact that acoustical studs achieve a higher degree of decoupling between the two surface layers, and the effect of the studs only exists in the frequency range above the bridging frequency. Meanwhile, the influence of the sound bridging effect generated by light steel studs can also extend to the low frequency range, not only in the high frequencies, and has a certain degree of influence on the sound insulation performance of the wall.
The influence of stud space of the double-leaf wall cases with the Rubber isolation acoustical studs (Case C5).
Figure 12 presents the influence of wall dimensions on the sound insulation performance of Case C5, with variations of 3.0 m × 2.4 m, 1.5 m × 1.2 m, and 0.75 m × 1.2 m, respectively. It is shown that the size effect on the airborne sound insulation performance of this configuration mainly exists in the low-frequency range below the bridging frequency. As the panel size decreases, the overall apparent bending stiffness of the wall increases accordingly, leading to a gradual shift of the mass-air-mass resonance frequency towards higher frequencies. Meanwhile, in the frequency range below this resonance, the wall is under the stiffness-controlled zone, and its sound insulation performance in this frequency range shows a significant improvement with the decrease in panel size. This indicates that, in practical application scenarios, the target requirement for low-frequency sound insulation can be met by adopting a modular approach and reasonably setting the dimensions of the unit walls to construct a full-size partition through the combination of multiple unit walls.
The influence of size of the double-leaf wall cases with the Rubber isolation acoustical studs (Case C5).
According to the study above, it is found that the double leaf wall with acoustical stud exhibits superior airborne-sound insulation performance. This can be primarily attributed to the acoustical studs’ ability to effectively decouple the two leaves, thereby mitigating the influence of the structure-borne sound transmission path on the overall sound insulation capacity. Consequently, double leaf walls with acoustical stud have great application potential in construction engineering, enabling the creation of thin partition walls with high soundproofing capacities. To demonstrate this point, this section presents an optimal configuration with the constrained layer damping composite surfaces. The design goal is to meet the requirements of the code of GB 50,118–201044 (Design of sound insulation of civil buildings), which stipulates that the single number evaluation value of the soundproofing partition between bedrooms should be greater than or equal to 45 dB. The innovative aspect of this work lies in designing a detailed diagram of the connection between the acoustical stud and the composite surfaces, producing a 1:1 scale sample, and subsequently conducting the airborne sound insulation experiments in the national standard laboratory. This process serves as a comprehensive test and application of the method presented in this paper.
Figure 13 shows the construction diagram of the double leaf wall configuration. The size is designed according to the criterion of modular coordination. The overall size is 1800 mm × 1200 mm with the area of 2.16 m2. And it is divided into 3-unit plates. The size of the unit plate is 600 mm × 1200 mm × 100 mm. The two sides of the sample are combined with 5-splints and 3-splints. The frame system mainly includes rubber isolation clip, main frame, secondary frame, acoustic studs and bolt accessories. In the assembly process, the acoustic studs are fixed and connected to the secondary frame by bolts. The rockwool is used to fill the cavity between two leaves (Fig. 14).
Section diagram of the optimal double-leaf wall configuration with the rubber isolation acoustical stud.
Manufacture photos of the optimal double-leaf wall configuration with the rubber isolation acoustical stud
According to the code of ISO 10,140–2:202145, the sample was subjected to the airborne-sound insulation test in the reverberation chamber. The sound transmission loss is calculated as follows
where \(R\) is sound transmission loss (dB), \(\overline{L}_{p1}\) is the average sound pressure level (dB) of the sound source room, \(\overline{L}_{p2}\) is the average sound pressure level (dB) of the receiving room, \(S\) is the specimen area (\(m^{2}\) ), and \(A\) is the sound absorption area (\(m^{2}\) ) of the receiving room.
As shown in Fig. 15, the main test equipment used are the 01 dB FUSION sound level meter and the DO12 full directional dodecahedron speaker. The sound level meter is used for data acquisition, and the 01 dB dBInside software platform is used for analysis and post-processing of the measured data. The measurement is performed using a white noise signal at a center frequency band of 1/3 octave from 50 to 5000 Hz. In all measurement bands, the sound source has sufficient sound power so that the sound pressure level of the receiving chamber is at least 15 dB higher than the background noise level of the receiving chamber. The sound pressure level in the source room and the receiving room in each frequency band, as well as the reverberation time and background noise were measured and recorded.
Photos of the airborne sound insulation experiment. (a) DO12 Omnidirectional dodecahedral loudspeaker; (b) The sample placement status; (c) and (d) The receiving point in the source room and receiving room.
Figure 16 presents the STL spectrum results of the test. The single number evaluation value [Rw (C, Ctr)] of experiment and analytical solution are 48(-2, -6) and 48(-1, -6), respectively. It can be observed that the prediction and experimental results exhibit high consistency in the investigated frequency bands, which in advance validates the reliability of the present analytical model. However, some discrepancies are observed in the low-frequency range, primarily due to experimental errors. These discrepancies mainly arise from two factors. First, in the low-frequency range, the longer wavelength leads to significant modal effects in the source room, making it challenging to achieve a perfectly diffuse sound field. Second, variations of samples during the fabrication process and installation conditions can also impact the sound insulation performance in the low-frequency range. Due to the resonance effect between the composite surface layer and the cavity, a mass-air-mass resonance valley appears in the frequency range of 50 Hz to 125 Hz, with the lowest value of about 30 dB. Furthermore, due to the large apparent bending stiffness of the composite surfaces, the coincidence frequency of the double-wall configuration lies beyond the frequency range of interest and is not reflected in this figure.
Comparison between the experimental and analytical results of the optimal double-leaf wall configuration with the acoustical stud.
Meanwhile, at frequencies higher than mass-air-mass resonance, the structure is primarily governed by the mass law, in which the damping is enhanced and the influence of the structure-borne sound transmission path is weakened by adding the elastic joints between the stud and the composite surface layer. In addition, the standing wave resonance effect can be effectively suppressed by filling the cavity with an appropriate amount of sound absorbing materials. The double leaf wall configuration with acoustical stud is developed to offer an efficient and practical solution for airborne sound insulation. This wall configuration not only satisfies high-grade sound insulation standards but also provides significant spatial advantages. Its compatibility with modular design and standardized construction makes it particularly suitable for prefabricated residential buildings, hospitals, and similar settings. By incorporating performance-driven building principles throughout the construction process, this approach effectively reduces overall building costs while simultaneously enhancing construction quality.
Lightweight double leaf walls have been widely adopted in the construction of residential buildings, open offices, hospitals, and other environments. However, their sound insulation performance of is generally poor and often fails to meet the high standards specified in design codes. This paper proposes an analytical model based on decoupling the sound transmission path, enabling architects to quickly predict the airborne sound insulation performance of commonly used wall configurations. The key features of this method include: a. Wide applicability, covering various stud types such as wood studs, light steel studs, and acoustic studs; b. Efficient prediction across the full audio frequency range of 50–5000 Hz in 1/3 octave bands; c. Ease of use, designed for building designers rather than professional acoustics researchers. The accuracy of the method has been validated using experimental data.
Based on case studies, the paper systematically explores the mechanism of the sound bridge effect in double leaf walls and reveals how different stud types impact sound insulation performance. Results show that the sound bridge effect originates from the structural sound transmission path created by the studs connecting the two leaves of the double leaf wall. To enhance acoustic performance, focus should be on designing stud configurations that effectively decouple the two leaves acoustically. Traditional wood studs, due to their more rigid framework, contribute more significantly to the sound bridge effect than steel studs. Double studs and staggered studs can reduce the sound bridge effect by separating the panels but increase wall thickness. Therefore, this paper proposes an optimized double leaf wall configuration with acoustic studs incorporating rubber sound isolation inserts, which achieves a weighted sound insulation rating meeting high-level sound insulation standard. This wall configuration offers significant spatial advantages and is suitable for modular design and standardized construction. It is especially applicable in prefabricated housing and hospital settings. By integrating building performance throughout the construction process, this approach helps lower overall building costs while improving construction quality. Future work will focus on incorporating new environmentally friendly materials and exploring new double leaf wall configurations that meet mechanical strength, thermal insulation, and high sound insulation performance requirements. Additionally, the use of artificial intelligence technologies will be explored to support the achievement of carbon neutrality goals.
The datasets generated during the current study are available from the corresponding author on reasonable request.
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This work is supported by the Natural Science Foundation of China (Grant No. 51408113) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20140632).
Natural Science Foundation of China (51408113); Natural Science Foundation of Jiangsu Province, China (BK20140632).
Key Laboratory of Urban and Architectural Heritage Conservation, Ministry of Education, School of Architecture, Southeast University, 2# Sipailou, Nanjing, 210096, China
Hequn min, bo wang & ting qu
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Conceptualization, Hequn Min; methodology, Hequn Min; software, Bo Wang; validation, Hequn Min, Bo Wang and Ting Qu; investigation, Hequn Min, Bo Wang and Ting Qu; resources, Hequn Min; writing—original draft preparation, Hequn Min, Bo Wang and Ting Qu; writing—review and editing, Hequn Min; visualization, Hequn Min, Bo Wang and Ting Qu; supervision, Hequn Min; project administration, Hequn Min; funding acquisition, Hequn Min. All authors have read and agreed to the published version of the manuscript.
The authors declare no competing interests.
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Min, H., Wang, B. & Qu, T. Airborne sound insulation performance of lightweight double leaf walls with different stud types. Sci Rep 14, 30584 (2024). https://doi.org/10.1038/s41598-024-82403-w
DOI: https://doi.org/10.1038/s41598-024-82403-w
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