I am a graduate student in acoustics at the University of Texas at Austin. Below is an ongoing collection of thoughts, musings, and projects on acoustics.
Table of Contents
Notes & musings
- Angle of Intromission: the angle of intromission is the angle that corresponds to perfect transmission of sound between two media. Its derivation is straightforward but was not discussed in class, so I have shown the steps that lead to David Blackstock's equation (B-14) in section 5.B.2.a.
- Concentric Pressure-Release Spheres: based on an Acoustics II homework problem, displayed here are numerically determined combinations of ka and kb that correspond to the eigenfrequencies for sound enclosed between two concentric pressure-release spheres. Bright spots on the surface plots correspond to eigenfrequencies.
- Double Pressure-Release Parallel Planes: here is the solution for (1) a radially pulsating cylindrical source of sound extending between two pressure-release parallel planes. Dr. Blackstock mentions this kind of waveguide on page 432 in Fundamentals of Physical Acoustics. He solves for (2) a radially pulsating cylindrical source between two rigid, parallel planes on page 430, and assigns the case of (3) a radially pulsating cylindrical source between one rigid boundary and one pressure-release boundary (a 0th-order model of sound in the ocean) as problem 12-13. Interestingly, case (1) and (3) excite many modes, but case (2) excites only the lowest mode.
- Fourier acoustics: in the i(kx - ωt) convention.
- Green's functions: I show that Green's functions are solutions of an inhomogeneous Helmholtz equation. [How to directly integrate the first integral on the left-hand-side of equation (2)]. Here I re-derive Morse and Ingard's integral equation (7.1.17). This is a derivation of the Sommerfeld radiation condition.
- Intensity integral: evaluation of the integral for intensity in David Blackstock's Fundamentals of Physical Acoustics, section 1E-3 (page 50).
- Linear Sound Speed Gradient: I use the calculus of variations to show that arcs of circles minimize the travel time between two points in a medium where the sound speed varies linearly (i.e., the upper ocean). This recovers the result in "Acoustics: An Introduction to its Physical Principles and Applications" by Allan D. Pierce, section 8-3.
- Radiation from General Axisymmetric Spherical Source: re-organized for clarity.
- Sound in General Axisymmetric Spherical Enclosure: following Dr. Hamilton's approach for radiation due to a general axisymmetric source.
- Thoughts on the 1D linear wave equation: thoughts from the first week of grad school. It turns out that d'Alembert, Euler, Bernoulli, and others had contentiously debated these very issues 250 years ago!
- Three-Medium-Problem Demystified I derive the pressure reflection and transmission coefficients of the three-medium problem in a way that makes sense to me.
- Virial theorem for string: a well-known result of Hamilton's formulation of classical dynamics that relates the average kinetic energy of a system to its virial. I have never seen it applied to waves on a string, but in Dr. Mark Hamilton's Acoustics I course, we arrived at a special case of the theorem that showed that the kinetic and potential energies are equal for progressive waves on a string. I derive and apply the virial theorem to show the more general result.