Elements of Waves in Fluids

Catalog description

Thermodynamic and hydrodynamic foundations of linear acoustics in fluids with applications to lumped-elements, reflection, refraction, radiation, attenuation, enclosures, and waveguides. The purpose of this course is to provide the foundation for understanding the behavior of waves in fluids in the "linear acoustic" limit for first-year graduate students entering the Graduate Program in Acoustics. The course provides a common ground for students coming from a broad range of varying undergraduate programs in sciences, engineering, mathematics, and the arts. This self-consistent foundation will be built upon an understanding of thermodynamics and the consequences for the behavior of gases and gas mixtures (i.e., ideal gas equations-of-state, heat capacity), and hydrodynamics (both dissipative and non-dissipative) as expressed from the Eulerian perspective. This perspective will be used to develop techniques for understanding oscillations in lumped-element acoustical networks that are smaller than the wavelength of sound and will be applied to extended media in which waves propagate, are reflected and transmitted through interfaces between media with different acoustical properties, and are refracted through media with continuously-varying acoustical properties. The same equations will be applied to the excitation of sound waves that propagate in 3-dimensions by vibrating bodies that are smaller than the wavelength of sound. Those results will be extended by superposition of such "compact sources" to produce both discrete and continuous one- and two-dimensional arrays. The directional properties and strength of such extended sources will be examined. The behavior of sound within 3-dimentional rectangular enclosures is studied via the method of "separation of variables" to identify the sound modes in such enclosures, their characteristic frequencies, and the selective excitation and detection of such modes. The frequency dependence of the density of modes is introduced to motivate the relationship between the modal and raytracing (i.e., ballistic) perspectives. The techniques of "statistical energy analysis" will be applied such enclosures to quantify architectural phenomena such as reverberation time and critical distance. Those results will be extended to non-rectangular enclosures and to rectangular and cylindrical waveguides, focusing on the concept of group and phase speed and the coupling of sources to planewave and higher-order waveguide modes. Attenuation of sound waves is also treated from the hydrodynamic perspective and results are derived for boundary-layer dissipation, classical thermoviscous sound absorption within bulk fluids, and the relaxation-time approximation is applied for sound absorption by chemical association-dissociation in seawater and the effects of humidity on collision-times in air. Problem sets that illustrate the theory and applications are a central component of this course.