Please navigate the html version of my thesis using the table of contents below or click here to download the pdf files.

Theoretical and experimental study of wave propagation in brass musical instruments

Jonathan A Kemp

A thesis submitted in fulfilment of the requirements
for the degree of Doctor of Philosophy
to the
University of Edinburgh

2002

Errata:
In Chapter 2, equation (2.100) should read:
$Z^{(0)} = (i D_3)^{-1} Z_c - D_2^{-1} Z_c (Z^{(1)} + (i D_3)^{-1} Z_c)^{-1} D_2^{-1} Z_c$
In Chapter 7, in the section called "Acoustic pulse reflectometry measurement with MLS excitation", the second paragraph should begin with:
MLS signals are inherently periodic with a period of $2^m-1$.
These changes have been made in the online html and pdf versions of my thesis.

• Abstract
• Declaration
• Acknowledgments
• Contents
• List of Figures
• List of Tables
• Introduction to the study of wind instrument acoustics
  • Background
  • Acoustic resonance
  • Exciting the air column
  • Input impedance
  • Input impedance measurement techniques
    • Frequency domain measurement
    • Acoustic pulse reflectometry
  • Calculation of the input impedance
    • Multimodal propagation
  • Aims and outline of thesis
  
  
• Multimodal propagation in acoustic horns
  • Introduction
  • Plane waves in a uniform section of tube
  • Plane waves at a change in cross-section
  • Multimodal equations in a uniform wave-guide
    • Solutions for a cylinder
      • Loss-less propagation
      • Lossy propagation
    • Solutions for a uniform rectangular duct
      • Loss-less propagation
      • Lossy propagation
  • Multimodal equations at a discontinuity
    • Solutions for circular cross-section
    • Solutions for rectangular cross-section
  • Method for calculation of input impedance
    • Projection across a discontinuity
    • Projection along a cylinder
  • Method for calculation of pressure field
  
  
• Radiation impedance
  • Introduction
  • Ideal open end condition
  • The piston approximation
    • Pressure radiation from a piston terminated in an infinite baffle
  • Pressure radiation from a duct terminated in an infinite baffle
  • Multimodal radiation impedance of a duct terminated in an infinite baffle
  • Multimodal radiation impedance of a cylindrical duct terminated in an infinite baffle
    • Analysis
    • Results
  • Multimodal radiation impedance of a rectangular duct terminated in an infinite baffle
    • Analysis
    • Results
  
  
• Numerical implementation of multimodal theory
  • Review of input impedance method
    • The radiation impedance matrix
    • Projecting the impedance matrix
  • Numerical implementation
  • Results for a trumpet section
  
  
• Acoustic pulse reflectometry
  • Introduction
  • Input impulse response
  • Input impedance from the input impulse
    response
  • Layer peeling bore reconstruction
    • Numerical implementation issues
    • Losses
  • Apparatus
  • Experimental measurement of the input
    impulse response
    • Deconvolution
  • Experimental measurement of the input
    impedance
  • DC offset
  • Experimental measurement of the bore
    profile
  
  
• Multimodal reflections
  • Introduction
  • Multimodal reflectance matrix
  • Multimodal reflectance of a single
    discontinuity
  • Multimodal input impulse response
  • Issues in multimodal bore reconstruction
    • Multimodal scattering matrix
    • Iteration method with multimodal control
  
  
• Improvements to pulse reflectometry
  • Introduction
  • The virtual DC tube method
  • Measuring longer objects
    • Source reflection cancellation method
  • Results
  • Maximum length sequences
    • Generating an MLS sequence
    • Auto-correlation property of MLS
    • Extracting the system impulse response from MLS measurement
    • Acoustic pulse reflectometry measurement with MLS excitation
  
  
• Conclusions
  • Achievement of aims
    • Aim 1
    • Aim 2
    • Aim 3
    • Aim 4
  • Future work
  
  
• Properties of Bessel functions
• Projection at a discontinuity
  • General expression
    • Pressure
    • Volume velocity
  • Projection matrix in cylindrical geometry
  
  
• Inductance method
• Bibliography
• About this document ...

To my Business Home Page: Kemp Acoustics

To my research page