Professor Mark F. Hamilton

M E 384N, Spring 2024

Walker Department of Mechanical Engineering

University of Texas at Austin

- Mathematical preliminary
- Linear systems theory
- 1D Fourier transform
- 2D spatial Fourier transform
- Transform theorems
- The angular spectrum
- Hankel transform
- Dirac delta functions
- Fourier acoustics
- Pressure source
- Velocity source
- Intensity
- Code
- Radiation from plate due to a 1D bending wave
- Generalization to elastic waves in isotropic solids
- Nearfield acoustical holography (NAH)
- Rayleigh integrals
- Angular spectrum of a spherical wave
- Derivation of the first Rayleigh integral using Fourier acoustics
- Derivation of the second Rayleigh integral using Fourier acoustics
- Fraunhofer approximation
- Fresnel approximation
- Focused sources
- Fresnel approximation
- Far field of Fresnel approximation
- Gaussian beams
- Circular piston
- Rectangular piston
- Derivation of parabolic equation
- Moving media
- Galilean transformation of wave equation
- Doppler effect
- Sound in ducts with uniform flow
- Refraction with flow
- Bending wave in flow
- Piston radiation into crossflow
- Periodic media
- Scattering

These are my class notes from Dr. Hamilton's lectures. My notes almost exactly follow the material presented in the lecture (aside from a few topics that have been re-arranged for conceptual consistency), and I have made some additional comments and linked references in deep blue. Also, the relevant quotations of famous physicists at the tops of the pages were my addition. Please send suggestions and corrections to:

Chirag Gokani

chiragokani [at] gmail.com

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