One-dimensional Acoustic Waveguide Research Articles

Transversal Anderson localization of sound in acoustic waveguide arrays

We present designs of one-dimensional acoustic waveguide arrays and investigate wave propagation inside. Under the condition of single identical waveguide mode and weak coupling, the acoustic wave motion in waveguide arrays can be modeled with a discrete mode-coupling theory. The coupling constants can be retrieved from simulations or experiments as the function of neighboring waveguide separations. Sound injected into periodic arrays gives rise to the discrete diffraction, exhibiting ballistic or extended transport in transversal direction. But sound injected into randomized waveguide arrays readily leads to Anderson localization transversally. The experimental results show good agreement with simulations and theoretical predictions.

Adaptive calibration of a three-microphone system for acoustic waveguide characterization under time-varying conditions.

The pressure and velocity field in a one-dimensional acoustic waveguide can be sensed in a non-intrusive manner using spatially distributed microphones. Experimental characterization with sensor arrangements of this type has many applications in measurement and control. This paper presents a method for measuring the acoustic variables in a duct under fluctuating propagation conditions with specific focus on in-system calibration and tracking of the system parameters of a three-microphone measurement configuration. The tractability of the non-linear optimization problem that results from taking a parametric approach is investigated alongside the influence of extraneous measurement noise on the parameter estimates. The validity and accuracy of the method are experimentally assessed in terms of the ability of the calibrated system to separate the propagating waves under controlled conditions. The tracking performance is tested through measurements with a time-varying mean flow, including an experiment conducted under propagation conditions similar to those in a wind instrument during playing.

An audible demonstration of the speed of sound in bubbly liquids

The speed of sound in a bubbly liquid is strongly dependent upon the volume fraction of the gas phase, the bubble size distribution, and the frequency of the acoustic excitation. At sufficiently low frequencies, the speed of sound depends primarily on the gas volume fraction. This effect can be audibly demonstrated using a one-dimensional acoustic waveguide, in which the flow rate of air bubbles injected into a water-filled tube is varied by the user. The normal modes of the waveguide are excited by the sound of the bubbles being injected into the tube. As the flow rate is varied, the speed of sound varies as well, and hence, the resonance frequencies shift. This can be clearly heard through the use of an amplified hydrophone and the user can create aesthetically pleasing and even musical sounds. In addition, the apparatus can be used to verify a simple mathematical model known as Wood’s equation that relates the speed of sound of a bubbly liquid to its void fraction.

Nonlinear surface acoustic waves: Theory

A theoretical description is given for the propagation of surface acoustic wave pulses in anisotropic elastic media subject to the influence of nonlinearity. On the basis of nonlinear elasticity theory, an evolution equation is presented for the surface slope or the longitudinal surface velocity associated with an acoustic pulse. It contains a non-local nonlinearity, characterized by a kernel that strongly varies from one propagation geometry to another due to the anisotropy of the substrate. It governs pulse shape evolution in homogeneous halfspaces and the shapes of solitary surface pulses that exist in coated substrates. The theory describing nonlinear Rayleigh-type surface acoustic waves is extended in a straightforward way to surface waves that are localized at a one-dimensional acoustic waveguide like elastic wedges.

Acoustic wave propagation in one-dimensional phononic crystals containing Helmholtz resonators

One-dimensional acoustic waveguide containing subwavelength-sized Helmholtz resonators is known to exhibit novel physical phenomena. However, no systematic theoretical study on this system has been carried out so far except on a few limited cases. We present a thorough theoretical calculation on the acoustic wave propagation in phononic crystals containing Helmholtz resonators without any geometrical size restrictions. The band structures, transmission spectra, and defect states are studied for diverse geometries using the interface response theory. It is shown that the acoustic band structure of the model is fundamentally different from the conventional acoustic–elastic cases and richer due to the coexistence of the resonant and the Bragg gaps. It is also shown that the presence of a defect resonator in the system can give rise to a localized mode inside the resonance gaps. The results clearly show that the presence of the Helmholtz resonators singly or periodically can play a prominent role in designing any acoustic band gap materials.

Experimental energetic analyses of an actively controlled one-dimensional acoustic waveguide

Technological development has made it possible to implement digital active noise control systems in real time. This work compares the performance of different adaptive control methods applied to a one-dimensional waveguide. The compared control methods are the frequency-domain filtered-X LMS using potential energy density and kinetic energy density as cost functions, and the active sound intensity control (ASIC), which uses active intensity as the cost function. The ASIC controller is implemented with both the P–U approach (measuring pressure and particle velocity at the same time) and the P–P approach (using two microphones to estimate the active intensity). The waveguide is a circular PVC duct with a primary source placed at one end, the secondary source placed near the mid-span of the duct, and with an open-ended termination. The analyses were performed comparing the results in terms of the potential energy density, the active intensity, and the acoustic power radiated by the sources. Moreover, it is shown how to choose suitable error sensors and their influence in the performance of the ASIC controller. The results show that the control methods achieved the same final result and, as expected, when the volume velocity of the secondary source was driven to the optimal volume velocity, the primary source and the secondary source radiated less acoustic power than the uncontrolled primary source. Besides, the sound intensity was effectively attenuated throughout the duct.

Energetic analysis of an actively controlled one-dimensional acoustic waveguide

The aim of this work is to show the energetic behavior when an active noise controller is applied in a one-dimensional waveguide, namely an ideal duct under the first critical frequency. In order to model the duct, a spectral element method, which is shown to be more practical for analyzing pipe networks than other commonly used analytical models, was used. The model used here consists of a duct with two sources, the primary source at one end of the duct, and the secondary source at the middle section. The error sensor was placed downstream from secondary source, and the other end of the duct was open with no flange. Three optimal control methods were applied: minimization of the potential energy density, minimization of the active intensity, and minimization of the total acoustic power radiated by the sources. It was observed that the three control methods achieved the same final result, and when the volume velocity of the secondary source was driven to the optimal volume velocity, neither the primary source nor the secondary source radiated any acoustic power. Furthermore, the controlled duct was equivalent to a duct opened-ended at the secondary source position with radiation impedance equal to zero.

Time-domain simulation of acoustical waveguides with arbitrarily spaced discontinuities

The multiconvolution algorithm [Martı́nez et al., J. Acoust. Soc. Am. 84, 1620–1627 (1988)] to calculate the impulse response or reflection function of a musical instrument air column has proved to be useful, but it has the limitation that the spacing between discontinuites is constrained to be some multiple of cΔt (for phase velocity c and time step Δt). This paper presents an improved method, the continuous-time interpolated multiconvolution (CTIM), where such a limitation has been removed. The response of an air column, modeled as an arbitrary one-dimensional acoustic waveguide constructed using cylindrical or conical bore segments with viscothermal damping and tone-hole discontinuities, is obtained through continuous-time convolutions between analytical reflection and transmission functions and discrete-time pressure signals. The arbitrary spacing between discontinuites is accounted for by interpolation of the discrete-time pressure signals. Many musical instrument air columns possess tone holes that are opened or closed so that tones of different pitches are produced. A time-domain calculation is presented of the acoustic responses of tone-hole discontinuities that may be open or closed. The resulting reflection and transmission functions are well suited for use in the CTIM.

Analogy between the one-dimensional acoustic waveguide and the electrical transmission line for cases with loss

Analogy between the one-dimensional acoustic waveguide and the electrical transmission line for lossless cases has been generalized to cases with loss.

On the analogy between the one-dimensional acoustic waveguide and the electrical transmission line

Equations for the electrical transmission line provide an analogy to the one-dimensional acoustic waveguide equations. The equations allow for either a pressure to voltage or a pressure to current analogy to be employed. The appropriate analogy to use is shown to be that of pressure to voltage.

Multiconvolution in waveguides with arbitrarily spaced discontinuities.

The multiconvolution algorithm [Martínez etal., J. Acoust. Soc. Am. 84, 1620–1627 (1988)] used to calculate the impulse response or reflection function of a musical instrument air column has proven to be useful, but it has the limitation that the spacing between discontinuities is constrained to be some multiple of c Δt (for phase velocity c and time step Δt). Two approaches have been devised to remove this limitation. Each time-domain approach calculates the response of an air column, modeled as an arbitrary one-dimensional acoustic waveguide constructed using cylindrical or conical bore segments with viscothermal damping and tone-hole discontinuities. The band-limited discrete-time multiconvolution (BDTM) specifies band-limited discrete-time reflection and transmission functions at each discontinuity. The continuous-time interpolated multiconvolution (CTIM) uses continuous-time convolutions between analytical reflection and transmission functions and discrete-time pressure signals. The arbitrary spacing between discontinuities is accounted for in the BDTM method by multirate discrete-time processing of the response functions, and in the CTIM method by interpolation of the discrete-time pressure signals.