[Websites] [Notes] [Practice problems] [Projects] [Crossword puzzles]
Acoustics PhD qualifying exam review site: website with everything I need to know for my qualifying exam.
ICA 2025 New Orleans: meeting website for the 25th International Congress on Acoustics and 188th Meeting of the Acoustical Society of America.
IntelliChoice SAT Math camp: this course originally served ~100 high school students in the DFW area during summer 2020 (COVID). Daily lessons and homeworks are now publicly available.
Wave Phenomena: my notes from Prof. Hamilton's course, spring 2024.
Bohr radius from variation principle: an elegant way of calculating the Bohr radius without looking at the Schrödinger equation. Based on class notes from Prof. Yuri Gartstein's Quantum I course at UTD.
Coriolis and centrifugal forces: slides on fictitious forces.
Fubini solution: The Fubini solution solves the lossless nonlinear approximate evolution equation (accurate to quadratic order) as a Fourier sine series from \(0 \leq \sigma < 1\), where \(\sigma\) is distance nondimensionalized by the shock-formation distance. The expansion coefficients \(B_n\) involve integrating over \(\theta\) from \(\theta = 0 \) to \(\theta = \pi\). The phase \(\Phi\) of the Fubini solution is given by the dimensionless phase of the lossless nonlinear approximate solution, \(\Phi = \theta + \sigma \sin(\Phi)\). This page answers the question, "Why does \(\Phi\) take on the same limits as \(\theta\) in the integration?"
Green's functions: working out the approach prescribed in Theoretical Acoustics by Morse and Ingard, I show that \(e^{ikR}/4\pi R\) solves the 3D inhomogeneous Helmholtz equation \((\Laplacian + k^2)f = -\delta(\vec{r}-\vec{r}_0)\). [How to directly integrate the first integral on the left-hand-side of Eq. (2)]. Here I re-derive Morse and Ingard's integral equation (7.1.17), which is the Helmholtz-Kirchhoff integral. This is a derivation of the Sommerfeld radiation condition. For more on Green's functions, see my notes from Prof. Hamilton's Wave Phenomena course.
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 (e.g., the upper ocean). This recovers the result in Acoustics: An Introduction to its Physical Principles and Applications by A. D. Pierce, Sec. 8-3.
Masala chai: traditional Indian tea
Planck quantities: based on Prof. Xiaoyan Shi's first Modern Physics lecture at UTD.
Radiation force: notes on how this force arises in mechanics, acoustics, and electrodynamics.
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!
Virial theorem for a string: the virial theorem is relates the average kinetic energy of a system to its virial. In Acoustics I, 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.
Acoustics I practice problem: an entertaining practice problem I wrote while studying for my Acoustics I midterm exam. It involves a "Gaussian comb" pressure-amplitude profile. [solution].
Acoustics I practice problem: created in preparation for the Acoustics I final. [solution].
Acoustics II practice problem: starring me and Jackson, created in preparation for the Acoustics II midterm. [solution]. My Acoustics I/II practice problems resulted in a conference talk that I presented at the 183rd ASA, Nashville, TN.
Multivariable calculus grad school skills seminar: a refresher worksheet on multivariable calculus for undergraduate and graduate students in acoustics at UT Austin. This worksheet was presented as an activity for the Austin Student Chapter of the ASA on November 15th, 2024.
Nonlinear acoustics study guide for midterm: problems that review the first half of Prof. Hamilton's nonlinear acoustics course. [solutions].
Nonlinear acoustics study guide for final: problems that review the second half of Prof. Hamilton's nonlinear acoustics course. [solutions].
Finite element replication of acoustic Dirac-like cone and double zero refractive index: term project for Prof. Michael Haberman's course on acoustic metamaterials, ME 397, fall 2021.
Pappus's theorem: interesting theorem derived for my end-of-semester group project in Prof. Mohammad Akbar's undergraduate geometry course at UTD, MATH 3321, summer 2020.
Theoretical analysis of ultrasonic vortex beam generation with single-element transducer and phase plate: term project for Prof. Michael Haberman's course on ultrasonics, ME/EE 384N, spring 2022.
Acoustics crossword for the 188th ASA & 25nd ICA conference: a crossword puzzle for conference participants
Acoustics crossword for WiSTEM: a crossword puzzle appropriate for high school students