Acoustic Waves Course

Lesson 1 • Speed of Sound in Media

Derives the speed of sound from bulk modulus and density for fluids and solids. Explains how temperature, pressure, and material properties alter propagation speed.

Lesson 2 • Energy and Intensity of Sound

Quantifies acoustic energy flux and introduces the decibel scale for intensity. Prepares students to measure and compare sound levels in practical contexts.

Lesson 3 • Sound as a Pressure Wave

Frames acoustic waves as oscillating pressure and density variations in a fluid medium. Connects particle motion to measurable pressure fluctuations central to acoustics.

Lesson 4 • Nature of Mechanical Waves

Introduces the concept of disturbance propagation through elastic media. Establishes the physical distinction between transverse and longitudinal motion as the basis for all acoustic study.

Lesson 1 • Fourier Analysis of Acoustic Signals

Applies Fourier series and transforms to decompose complex waveforms into spectral components. Connects time-domain signals to frequency-domain representations used in measurement.

Lesson 2 • The One-Dimensional Wave Equation

Derives the 1-D wave equation from Newton's second law and the continuity equation. Establishes the PDE framework that underpins all subsequent analytical work.

Lesson 3 • Acoustic Impedance

Defines specific acoustic impedance as the ratio of pressure to particle velocity. Shows how impedance governs energy transmission and reflection at interfaces.

Lesson 4 • Complex Notation and Phasors

Introduces complex exponential representation to simplify harmonic wave analysis. Enables efficient manipulation of amplitude and phase in multi-component problems.

Lesson 1 • Normal Incidence at Plane Interfaces

Derives pressure and intensity reflection and transmission coefficients for waves striking an interface perpendicularly. Establishes the impedance-matching principle.

Lesson 2 • Mode Conversion at Solid Interfaces

Introduces conversion between longitudinal and shear waves at solid boundaries. Relevant to ultrasonic testing and seismic wave analysis.

Lesson 3 • Reflection from Rigid and Soft Boundaries

Contrasts reflection behaviour at pressure-release and rigid surfaces as limiting impedance cases. Explains phase reversal and its effect on standing wave formation.

Lesson 4 • Transmission Through Layered Media

Analyses multi-layer systems using transfer matrix methods to find net transmission. Applies results to noise barriers, underwater sediment layers, and building partitions.

Lesson 1 • Formation of Standing Waves

Shows how two counter-propagating waves superpose to create nodes and antinodes. Derives standing wave patterns for pressure and particle velocity.

Lesson 2 • Resonance in Rectangular Rooms

Extends 1-D resonance to three-dimensional rectangular enclosures using modal analysis. Identifies axial, tangential, and oblique room modes.

Lesson 3 • Damping and Quality Factor

Introduces viscous and radiation damping mechanisms that limit resonance amplitude. Defines the quality factor Q and relates it to bandwidth and decay rate.

Lesson 4 • Resonance in Tubes and Pipes

Derives resonant frequencies for open, closed, and half-open cylindrical tubes. Connects boundary conditions to harmonic series and musical acoustics.

Lesson 1 • Scattering from Simple Objects

Introduces scattering cross-section and the Rayleigh and geometric scattering regimes. Applies results to bubbles, particles, and biological tissue in ultrasound.

Lesson 2 • Interference and Superposition

Analyses constructive and destructive interference from multiple coherent sources. Derives path-length difference conditions for maxima and minima.

Lesson 3 • Huygens' Principle and Diffraction

Applies Huygens' principle to explain wave bending at apertures and edges. Derives the conditions under which diffraction is significant relative to wavelength.

Lesson 4 • Diffraction Gratings and Arrays

Extends multi-source interference to periodic arrays and diffraction gratings. Derives grating equations and connects them to phased array beam steering.

Lesson 1 • Radiation from Vibrating Surfaces

Applies the Rayleigh integral to compute radiation from planar baffled sources. Introduces radiation efficiency and its dependence on surface velocity distribution.

Lesson 2 • Directivity and Beam Patterns

Defines directivity index and directivity factor for acoustic sources. Analyses how source geometry and frequency shape the radiated beam.

Lesson 3 • Point Sources and Monopoles

Derives the pressure field of a pulsating sphere in the limit of small radius. Establishes the monopole as the fundamental building block for source modelling.

Lesson 4 • Dipole and Multipole Sources

Constructs dipole and quadrupole sources from monopole superposition. Explains directivity patterns and reduced radiation efficiency at low frequencies.

Lesson 1 • Attenuation in Solids and Tissues

Extends absorption analysis to viscoelastic solids and biological tissue. Introduces the power-law attenuation model widely used in ultrasound imaging.

Lesson 2 • Absorption Mechanisms in Fluids

Identifies viscous, thermal, and molecular relaxation losses as the primary absorption mechanisms. Derives the classical absorption coefficient and its frequency dependence.

Lesson 3 • Propagation in Inhomogeneous Media

Analyses refraction and ducting caused by gradients in sound speed. Applies ray theory to predict propagation paths in the ocean and atmosphere.

Lesson 4 • Dispersion and Group Velocity

Distinguishes phase velocity from group velocity in dispersive media. Analyses pulse spreading and its implications for signal fidelity in guided wave systems.

Lesson 1 • Sound Level Meters and Weighting

Describes the architecture of a sound level meter and the purpose of frequency weighting networks. Connects measurement standards to occupational and environmental noise assessment.

Lesson 2 • Uncertainty and Calibration in Acoustics

Identifies sources of measurement uncertainty and establishes calibration procedures for acoustic instruments. Applies uncertainty propagation to reported measurement results.

Lesson 3 • Microphones and Transducer Principles

Explains the operating principles of condenser, electret, and piezoelectric microphones. Covers sensitivity, frequency response, and directional characteristics relevant to field use.

Lesson 4 • Impulse Response and Transfer Functions

Measures room and system impulse responses using swept-sine and MLS excitation. Derives transfer functions and extracts acoustic parameters such as reverberation time.