Nonclassical acoustics

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows

Effects of friction and heat conduction on sound propagation in ducts

The theory of sound propagation is examined in a viscous, heat-conducting fluid, initially at rest and in a uniform state, and contained in a rigid, impermeable duct with isothermal walls. Topics covered include: (1) theoretical formulation of the small amplitude fluctuating motions of a viscous, heat-conducting and compressible fluid; (2) sound propagation in a two dimensional duct; and (3) perturbation study of the inplane modes

Long-lived Magnetic-Tension-Driven Modes in a Molecular Cloud

We calculate and analyze the longevity of magnetohydrodynamic (MHD) wave modes that occur in the plane of a magnetic thin sheet. Initial turbulent conditions applied to a magnetically subcritical cloud are shown to lead to relatively rapid energy decay if ambipolar diffusion is introduced at a level corresponding to partial ionization primarily by cosmic rays. However, in the flux-freezing limit, as may be applicable to photoionized molecular cloud envelopes, the turbulence persists at "nonlinear" levels in comparison with the isothermal sound speed \cs, with one-dimensional rms material motions in the range of \approx 2\,\cs -5\,\cs for cloud sizes in the range of \approx 2\,\pc - 16\,\pc. These fluctuations persist indefinitely, maintaining a significant portion of the initial turbulent kinetic energy. We find the analytic explanation for these persistent fluctuations. They are magnetic-tension-driven modes associated with the interaction of the sheet with the external magnetic field. The phase speed of such modes is quite large, allowing residual motions to persist without dissipation in the flux-freezing limit, even as they are nonlinear with respect to the sound speed. We speculate that long-lived large-scale MHD modes such as these may provide the key to understanding observed supersonic motions in molecular clouds.Comment: Accepted by The Astrophysical Journal, 6 pages, 5 figures. Animations and a 3D pdf file are available at http://www.astro.uwo.ca/~basu/pb.ht

Discussion of the De Generatione Sonorum, a treatise on sound and phonetics by Robert Grosseteste

Here I am proposing a translation and discussion of the De Generatione Sonorum, one of the short scientific treatises written by Robert Grosseteste. The subject is the sound and the phonetics. In this treatise we find a discussion of oscillations and elasticity of materials and the description of some motions and their combinations to

Correlating Infall with Deuterium Fractionation in Dense Cores

We present a survey of HCO+ (3-2) observations pointed towards dense cores with previous measurements of N(N2D+)/N(N2H+). Of the 26 cores in this survey, five show the spectroscopic signature of outward motion, nine exhibit neither inward nor outward motion, eleven appear to be infalling, and one is not detected. We compare the degree of deuterium fractionation with infall velocities calculated from the HCO+ spectra and find that those cores with [D]/[H] > 0.1 are more likely to have the signature of inward motions than cores with smaller [D]/[H] ratios. Infall motions are also much more common in cores with masses exceeding their thermal Jeans masses. The fastest infall velocity measured belongs to one of the two protostellar cores in our survey, L1521F, and the observed motions are typically on the order of the sound speed.Comment: Accepted to Ap