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Granular materials display significant differences in their acoustical response when tested in a standing wave tube, compared with the behavior of more traditional sound absorbing materials such as fibrous webs and foams. The latter materials can often be modeled as an equivalent fluid with the further assumption that the material properties do not depend on the input signal level. In contrast, the level dependence of the acoustical behavior of granular materials has been observed in measurements of glass bubbles, as reported in previous studies, for example. When the input level is low, the absorption coefficient of the glass bubble stack shows solid-like behavior with multiple peaks associated with modal response of the stack. On the other hand, when the input level is high, glass bubble stacks show fluid-like behavior, with the quarter wavelength resonance in the direction of the tube axis dominating the response. In the current work, the boundary conditions at the air/granule interface and the granule/tube wall boundary are studied, as is the mechanism causing the variation of the apparent stiffness of the granule stack. The proposed model is implemented with a finite difference approach, and the model predictions are compared with acoustic measurements of granule stacks.

Because of the high sound absorption they offer at low frequencies, there is a growing interest in high surface area particles and how they might be applied in noise control. Therefore, a model that can accurately predict the acoustic behavior of this type of materials will be useful in relevant applications. A poro-elastic model based on a combination of Biot theory and an existing rigid model of granular activated carbon (GAC) is introduced in the current work. The input parameters for this model consist of a certain number of properties that are known by measurement, and a set of values obtained by matching the model prediction with acoustic measurements. Measured absorption coefficients and surface impedance of stacks of several types of different activated carbon particles are shown in this paper. A fitting procedure that determines the unknown parameters is also described. It is shown that the model is able to predict the acoustic behavior of the particle stacks, and especially to capture the frame resonances at low frequencies, thus, validating the proposed model. Beyond the activated carbon used in the present tests, it is reasonable to generalize this model to stacks of other high surface area particles.

In this article, a general method is proposed to model layered systems with two-by-two transfer matrices, and further, to solve for the acoustic absorption, reflection, and transmission coefficients. Since the proposed method uses the matrix representation of various layers and interfaces from the Transfer Matrix Method (TMM), the equation system can be established efficiently. However, the traditional TMM can lose stability when there is a large disparity between the magnitudes of the waves traveling in opposite directions within the layers (i.e., at higher frequencies, for a thick layer, or for extreme parameter values). In such cases, the contribution of the most attenuated wave can be masked by numerical errors and can induce instability when solving the system. Therefore, in the proposed method, to stabilize the calculated acoustic properties of the system, the principle is to ensure the accuracy of the wave attenuation terms by decomposing each layer's transfer matrix and reformulating the equation system. This method can couple different layer types in a general way and is easy to assemble and implement with numerical code. The predicated acoustic properties of layered systems calculated using the proposed method have been validated by comparison with those predicted by other existing methods.

In this work, an iterative method based on the four-microphone transfer matrix approach was developed for evaluating the sound speed and attenuation constant of air within a standing wave tube. When the air inside the standing wave tube is treated as the material under test, i.e., as if it were a sample of porous material, the transfer matrix approach can be used to identify the air's acoustic properties. The wavenumber within the tube is complex owing to the formation of a visco-thermal boundary layer on the inner circumference of the tube. Starting from an assumed knowledge of the air properties, an iterative method can be applied in the post-processing stage to estimate the complex wavenumber. Experimental results presented here show that although the results are sensitive to ambient temperature, a semi-empirical formula previously proposed by Temkin [(1981). Elements of Acoustics (John Wiley & Sons)] matches closely with the measured sound speed and attenuation constant, as does a theoretical formulation proposed by Lahiri et al. [(2014). J. Sound Vib. 333(15), 3440–3458]. Further, it is shown that the Temkin [(1981). Elements of Acoustics (John Wiley & Sons)] and Lahiri et al. [(2014). J. Sound Vib. 333(15), 3440–3458] predictions accurately represent the variation of sound speed with frequency, in contrast to the formula recommended in the ASTM E1050 standard [(2019). American Society for Testing and Materials], in which the sound speed is assumed to be independent of frequency.

In the present work, an iterative method based on the four-microphone transfer matrix approach was developed for evaluating the sound speed and attenuation constant of air within a standing wave tube. In particular, when the air inside the standing wave tube is treated as the material under test, i.e., as if it were a sample of porous material, the transfer matrix approach can be used to identify the air’s acoustic properties. Note that the wavenumber within the tube is complex owing to the formation of a visco-thermal boundary layer on the inner circumference of the tube. Starting from an assumed prior knowledge of the air properties, an iterative method can be applied in the post-processing stage to estimate the complex wavenumber accurately. Experimental results presented here show that although the results are sensitive to ambient temperature, a formula previously proposed by Temkin matches closely with the measured sound speed and attenuation constant. Furthermore, it is shown that the Temkin prediction accurately represents the variation of sound speed with frequency, in contrast to the formula recommended in the ASTM E1050 standard, in which the sound speed is assumed to be independent of frequency.

Tonal noise from rotating machinery is known to be a problem in buildings. To guide the design of a comfortable office environment, a proper understanding of people’s annoyance due to exposure to tonal office noise is valuable. Earlier, authors have proposed and verified two annoyance prediction models based on the psychoacoustic subjective tests conducted in an office mock-up, and further developed a software to implement the metric models. In the present work, the focus is shifted to some unexpected response variations observed while analyzing the responses from subjective tests: (1) the learning pattern that occurs at the beginning of the test; (2) the significant differences in the averaged annoyance ratings with respect to the gender and the Noise-Sensitivity-Questionnaire (NoiSeQ) score; (3) the acclimation to sounds: i.e., the annoyance ratings for the 2-min sounds were lower than the ratings for the corresponding 5-s sounds; and (4) the inconsistencies in ratings: i.e., subjects tend to use the annoyance scale differently in different parts of the test and to rate sounds relative to the background level in the room. In the end, several approaches to deal with these response variations and a few recommendations on the psychoacoustic test design are summarized.

Researchers have previously observed elastic modulus softening and increased damping when granular particle stacks are exposed to progressively increasing acoustical excitation levels. However, the level-dependent behavior of granular particle stacks is not well understood, and there are no comprehensive approaches to modeling those effects. Earlier, the authors measured the absorption coefficient of a stack of one type of granular activated carbon stack by using signals having different bandwidths and levels. In the present work, five more types of granular particle stacks were studied to validate and generalize the previous conclusions: i.e., both the modulus softening, and increased damping can be characterized by the total RMS fluid displacement at the sample surface. Therefore, a strain-dependent modulus and damping formula from the literature (based on cyclic loading tests on sand particles) was converted into a total RMS fluid displacement-dependent formula (based on acoustic measurements). In addition, a multi-layered model based on this displacement-dependent formula has been developed to iteratively update each layer’s modulus, damping, and total RMS fluid displacement to solve for the particle stack’s acoustic properties. This approach allows modeling of the particle stack’s acoustical behavior by using a single set of parameters, even for different level and bandwidth test signals.

Recently, it has been observed that a particle stack’s elastic modulus and damping change with incident levels. Hence, the measured normal incidence absorption coefficient also varies: i.e., the quarter-wave resonance peak shifts to a lower frequency and grows broader under progressively higher incident sound levels. Therefore, models with strain-dependent modulus and damping have been developed for sand particles based on a series of cyclic triaxial tests, while more recently, a velocity-dependent modulus was proposed to model the acoustically induced elastic softening for the hollow glass beads. To investigate the nature of this nonlinear behavior, the absorption coefficients of a 30 mm carbon particle stack were measured under four types of band-passed input signals (i.e., 500–1000 Hz, 500–2000 Hz, 500–4000 Hz, and 500–8000 Hz), each with 15 levels in steps of 1 dB. The input signals were designed to span the resonance frequency and to extend beyond to various degrees. The integrated sound pressure level, velocity, and displacement at the particle stack surface were calculated and were used to normalize the changing modulus and damping. It was found that only the total rms surface displacement can align the changing properties for all measurements.

Tonal sounds are a particular problem of concern in building environments, arising from the widely used rotating machinery (e.g., compressors, fans, motors, trans- formers, etc.). In the recent trend of designing and manufacturing high-performance building mechanical systems, higher output power and higher rotation speed are pursued, this inevitably results in a more severe noise problem, since the equipment noise not only becomes louder but also shifts to a higher frequency region (which, in most cases, results in a poorer sound quality due to the shift in spectral balance and tonal components moving into the frequency regions where people are most sensitive to tones). Tonal sounds from rotary machines can be annoying, even at relative low levels.Currently, noise criteria guidelines in Chapter 48 of the ASHRAE HVAC Applications Handbook can be used to design the building mechanical system, but this does not apply well for tonal noise. Reducing the limit for noise with perceptible tones is one common strategy in the industry. However, it’s not adequate for some cases, over-design in others. Thus, an adequate understanding of the annoyance threshold of tonal noises associated with building services equipment is valuable technical information not only in the design and manufacture of machines but also in the development of noise regulations related to building services equipment.This research aims to develop a sound quality model that cooperates with sound level and tonalness and relates tonal building noises to the perceived annoyance.

The purpose of sound field reproduction is to use loudspeakers to produce desired sound at particular locations in a given environment, which has a wide range of applications such as virtual reality, etc. The computational load required to design and implement filters involved in sound reproduction systems can be significant, especially when the desired sound has rich information over a wide frequency band. To reduce the computational load, sub-band filtering approaches are usually used in sound reproduction systems. In the present work, an approach is proposed to design the sub-band filters used in sound reproduction systems in a more convenient way, where the filter design problem is formulated into a convex optimization problem. Detailed analysis has been conducted on how to specify the response characteristics of each sub-band and how different sub-band filters can be combined into one full band filter in the design and implementation of the system. Results also show that even if the sub-band filter structure is not necessary, this approach can also be applied to reduce the computational load in designing inverse filters when the plant responses involve relatively large differences in delay time among different frequency bands.