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) (and also the same equation in Chapter 4, equation (4.6)) should read:

The original print of my thesis has these equations as:

This original version is mathematically wrong (as it assumes diagonal impedance matrices).
The difference is minimal in terms of calculation results for approximating a bore with high numbers of cylinders.

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 .

The above changes have been made in the online html and pdf versions of my thesis.

Equation 6.24 appears to be wrong in my thesis and corrections/devivations have been given by Bjørn Kolbrek. Please download Bjørn Kolbrek's corrections.

- 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
- Calculation of the input impedance
- 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
- Multimodal equations at a discontinuity
- Method for calculation of input impedance
- Method for calculation of pressure field

- Radiation impedance
- Introduction
- Ideal open end condition
- The piston approximation
- 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
- Multimodal radiation impedance of a rectangular duct terminated in an infinite baffle

- Numerical implementation of multimodal theory

- Acoustic pulse reflectometry
- Introduction
- Input impulse response
- Input impedance from the input impulse

response - Layer peeling bore reconstruction
- Apparatus
- Experimental measurement of the input

impulse response - 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

- Improvements to pulse reflectometry

- Conclusions

- Properties of Bessel functions
- Projection at a discontinuity

- Inductance method
- Bibliography
- About this document ...

My Research Portal entry at the University of St Andrews.

Jonathan Kemp 2003-03-24