Educational resources

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 (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.

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, electrodynamics, and acoustics.

"Simplicity" by William Zinsser: from On Writing Well: An Informal Guide to Writing Nonfiction (1980).

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.

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.