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Journal of the Acoustical Society of America

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Apr 2005

Volume 117, Issue 4, pp. 1675-2625

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Linear and nonlinear propagation of higher order modes in hard-walled circular ducts containing a real gas

Stefan Scheichl

J. Acoust. Soc. Am. Volume 117, Issue 4, pp. 1806-1827 (2005); (22 pages)

Online Publication Date: 08 Apr 2005

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This paper deals with the linear and nonlinear propagation of sound waves through a real gas contained in a circular tube with rigid, isothermal walls. Special emphasis is placed on the asymptotically correct treatment of the higher order modes and their interaction with the acoustic boundary layer. In the first part, a linear perturbation analysis is carried out to calculate the correction terms arising from the viscothermal damping mechanisms present in the system. In extension to previous work, the propagation length is assumed to be so large that the exponentially growing boundary layer effects do not only affect the second order terms of the sound pressure but also the leading order terms. The series expansions derived for the propagation parameters extend the results given in the literature with additional terms resulting from viscosity and heat conduction in the core region. The second part is concerned with the nonlinear modulation of a wave packet transmitted through a real gas. A damped nonlinear Schrödinger equation is derived and its solutions for positive as well as negative values of the nonlinearity parameter are studied. In particular, the case of wave propagation in ducts containing a so-called BZT fluid is discussed. © 2005 Acoustical Society of America.
Show PACS
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.25.Ba Parameters of nonlinearity of the medium
43.20.Mv Waveguides, wave propagation in tubes and ducts

Simultaneous measurement of acoustic and streaming velocities in a standing wave using laser Doppler anemometry

Michael W. Thompson and Anthony A. Atchley

J. Acoust. Soc. Am. Volume 117, Issue 4, pp. 1828-1838 (2005); (11 pages) | Cited 6 times

Online Publication Date: 08 Apr 2005

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Laser Doppler anemometry (LDA) with burst spectrum analysis (BSA) is used to study the acoustic streaming generated in a cylindrical standing-wave resonator filled with air. The air column is driven sinusoidally at a frequency of approximately 310 Hz and the resultant acoustic-velocity amplitudes are less than 1.3 m/s at the velocity antinodes. The axial component of fluid velocity is measured along the resonator axis, across the diameter, and as a function of acoustic amplitude. The velocity signals are postprocessed using the Fourier averaging method [Sonnenberger et al., Exp. Fluids 28, 217–224 (2000)]. Equations are derived for determining the uncertainties in the resultant Fourier coefficients. The time-averaged velocity-signal components are seen to be contaminated by significant errors due to the LDA/BSA system. In order to avoid these errors, the Lagrangian streaming velocities are determined using the time-harmonic signal components and the arrival times of the velocity samples. The observed Lagrangian streaming velocities are consistent with Rott’s theory [N. Rott, Z. Angew. Math. Phys. 25, 417–421 (1974)], indicating that the dependence of viscosity on temperature is important. The onset of streaming is observed to occur within approximately 5 s after switching on the acoustic field. © 2005 Acoustical Society of America.
Show PACS
43.25.Nm Acoustic streaming

Influences of a temperature gradient and fluid inertia on acoustic streaming in a standing wave

Michael W. Thompson, Anthony A. Atchley, and Michael J. Maccarone

J. Acoust. Soc. Am. Volume 117, Issue 4, pp. 1839-1849 (2005); (11 pages) | Cited 4 times

Online Publication Date: 08 Apr 2005

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Following the experimental method of Thompson and Atchley [J. Acoust. Soc. Am. 117, 1828–1838 (2005)] laser Doppler anemometry (LDA) is used to investigate the influences of a thermoacoustically induced axial temperature gradient and of fluid inertia on the acoustic streaming generated in a cylindrical standing-wave resonator filled with air driven sinusoidally at a frequency of 308 Hz. The axial component of Lagrangian streaming velocity is measured along the resonator axis and across the diameter at acoustic-velocity amplitudes of 2.7, 4.3, 6.1, and 8.6 m/s at the velocity antinodes. The magnitude of the axial temperature gradient along the resonator wall is varied between approximately 0 and 8 K/m by repeating measurements with the resonator either surrounded by a water jacket, suspended within an air-filled tank, or wrapped in foam insulation. A significant correlation is observed between the temperature gradient and the behavior of the streaming: as the magnitude of the temperature gradient increases, the magnitude of the streaming decreases and the shape of the streaming cell becomes increasingly distorted. The observed steady-state streaming velocities are not in agreement with any available theory. © 2005 Acoustical Society of America.
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43.25.Nm Acoustic streaming

On the interaction of counterpropagating acoustic waves in resonant rods composed of materials with hysteretic quadratic nonlinearity

Vitalyi Gusev

J. Acoust. Soc. Am. Volume 117, Issue 4, pp. 1850-1857 (2005); (8 pages) | Cited 1 time

Online Publication Date: 08 Apr 2005

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An ordinary inhomogeneous integrodifferential equation for the profile of the acoustic wave in a resonant rod, composed of a material with hysteretic quadratic nonlinearity, is derived. It explicitly takes into account the interaction of the counterpropagating acoustic waves. It also incorporates the boundary conditions in the sense that all possible solutions of the equation satisfy the appropriate boundary conditions at the ends of the rod. © 2005 Acoustical Society of America.
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43.25.-x Nonlinear acoustics
43.25.Lj Parametric arrays, interaction of sound with sound, virtual sources
43.25.Gf Standing waves; resonance

On the stability of the effective apodization of the nonlinearly generated second harmonic with respect to range

Russell J. Fedewa, Kirk D. Wallace, Mark R. Holland, James R. Jago, Gary C. Ng, Brent S. Robinson, Matthew R. Rielly, and James G. Miller

J. Acoust. Soc. Am. Volume 117, Issue 4, pp. 1858-1867 (2005); (10 pages)

Online Publication Date: 08 Apr 2005

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The concept of an effective apodization was introduced to describe the field pattern for the nonlinearly generated second harmonic (2f) within the focal zone using a linear propagation model. Our objective in this study was to investigate the validity of the concept of an effective apodization at 2f as an approach to approximating the field of the second harmonic over a wide range of depths. Two experimental setups were employed: a vascular imaging array with a water path and an adult cardiac imaging array with an attenuating liver path. In both cases the spatial dependencies of the ultrasonic fields were mapped by scanning a point-like hydrophone within a series of planes orthogonal to the propagation direction. The sampling distances were located before, within, and beyond the focal zone. The signals were Fourier transformed and the complex values at 2f were linearly backpropagated to the transmit plane in order to obtain an effective apodization. The measured results demonstrated a relatively constant effective apodization at 2f as a function of propagation distance. Finite amplitude computer simulations were found to be in agreement with these measurements. Thus the measure of the effective apodization at 2f provides an approximation to the second harmonic field outside the focal zone. © 2005 Acoustical Society of America.
Show PACS
43.25.-x Nonlinear acoustics
43.25.Jh Reflection, refraction, interference, scattering, and diffraction of intense sound waves
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
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