The aims of this thesis are:

1. to study and develop the theory of multimodal propagation in acoustic horns, in order to enable the influence of higher mode propagation to be assessed.

2. to describe acoustic pulse reflectometry as a means of measuring the properties of brass musical instruments, and to perform experiments to give examples of its use.

3. to develop acoustic pulse reflectometry to enable the measurement of longer instruments and to speed up the measurement process.

4. to discuss the possibility of including higher modes in the analysis of pulse reflectometry data.

Chapter 2 consists of a review of the theory of wave propagation in tubular objects first assuming plane wave propagation and then using multimodal expressions. This material is a review with amendments and corrections of the method of Pagneux et al. [32] for waveguides of circular cross-section and new work for objects of rectangular cross-section is also presented. A method for the calculation of the input impedance and pressure field is then derived.

In order to perform a multimodal calculation of the input impedance, the radiation impedance (the impedance at the open end of the horn) is needed as a starting point. Chapter 3 presents a numerical method for its calculation. The method for pipes of cylindrical cross-section is due to Zorumski [37] while the results for pipes of rectangular cross-section is due to the current author [39]. Chapter 4 brings chapters 2 and 3 together, giving an example calculation of the input impedance and pressure field calculations for the bell section of a trumpet.

Chapter 5 is a review of acoustic pulse reflectometry. Experimental measurements of the input impulse response, the input impedance and the bore reconstruction are presented together with the analysis techniques.

In chapter 6 the multimodal reflection of sound from a single discontinuity between two infinite pipes is considered. The reflection is frequency dependent, with theoretical results presented showing the reflectance as a function of frequency and the time domain response. Analysis of pulse reflectometry experiments currently assumes plane wave propagation. A discussion of the possibility of incorporating multimodal propagation in the pulse reflectometry bore reconstruction algorithm then follows.

In chapter 7 we discuss and implement various improvements to pulse reflectometry. The first of these simply makes an existing process for removal of a dc offset in the measurement more accurate and convenient. Next we increase the length of instruments that may be measured by using post-processing to remove unwanted interference due to reflection of sound from the source. Finally we investigate the use of maximum length sequences, pseudo random signals resembling white noise, which are used to increase the signal to noise ratio in measurements.

Chapter 8, which concludes the thesis, gives an overview of the achievement of the aims and suggests ideas for future work.

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