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
    • Solutions for a uniform rectangular duct
  • 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