List of Figures

1. Uniform pipe
2. Detail of a waveguide consisting of straight sections of length $d$ joined discontinuously
3. Cylindrical waveguide with radius $R$
4. Three dimensional plot of the Bessel function of the first kind of order 0 against radius on the $x$-$y$ plane
5. The Bessel function of the first kind of order 0
6. The modes in a cylindrical duct with $n = 0$ (plane wave mode), $n = 1$, $n = 2$ and $n = 3$ (evanescent). All have the same free space wavenumber
7. Rectangular waveguide with halfwidths $a$ and $b$
8. Horn approximated by a series of cylinders
9. Pressure field of a piston driven cylinder terminated in an infinite cylindrical pipe
10. Piston in an infinite baffle
11. Normalised direct radiation impedance of the $n$th mode in a circular duct of radius $R$ for $n=0,1,2.$
12. Coupled radiation impedances of a circular duct of radius R
13. Geometry of infinitely flanged rectangular duct
14. Radiation impedances of square and circular ducts
15. Direct radiation impedances of square ducts
16. Coupled radiation impedances of square ducts
17. Effect of aspect ratio on radiation impedances of rectangular ducts
18. Detail of a waveguide consisting of straight sections of length $d$ joined discontinuously
19. Trumpet section input impedance
20. Trumpet section input impedance
21. Trumpet section input impedance
22. Trumpet section pressure field: (a) plane wave approximation, (b) 2 modes, (c) 3 modes, (d) 5 modes, (e) 11 modes
23. Trumpet section pressure field: 11 modes
24. Travelling waves in a typical object split into cylindrical sections
25. Schematic diagram of the apparatus
26. The acoustic pulse reflectometer
27. Object reflections
28. Stepped tube connected to source tube
29. Calibration pulse
30. Input impulse response
31. Stepped cylinder test object input impedance
32. Trumpet section input impedance
33. Stepped tube connected to source tube through dc tube
34. Object reflections using dc tube
35. Reconstruction of test object consisting of stepped cylinders
36. Plane reflectance for a single discontinuity with $R_1/R_2=0.5$
37. Plane reflectance for a single discontinuity with $R_1/R_2=0.5$ showing high frequency behaviour
38. Plane reflection spectrum for different discontinuity ratios against $kR_1$
39. Plane reflection spectrum for different discontinuity ratios against $kR_2$
40. Plane input impulse response calculated for a single discontinuity with $R_1/R_2=0.5$
41. Object reflections using virtual dc tube
42. Reconstruction of test object consisting of stepped cylinders
43. Calibration pulse including source reflections
44. Reflections from long stepped cylinder test object including source reflections
45. Second half of long stepped cylinder test object reflections
46. Long stepped cylinder test object reflections
47. French horn object reflections
48. French horn bore reconstruction, first 3.5 metres
49. French horn bore reconstruction, first 4.3 metres
50. Feedback shift register and recurrence relation for $m$ = 4
51. Microphone signal for excitation with a $m=15$ MLS signal repeated twice
52. Microphone signal chopped to show one period of response to continuous excitation with a $m=15$ MLS signal
53. System impulse response
54. Calibration pulse isolated from system impulse response
55. Object reflections isolated from system impulse response
56. Reconstructions for different orders of MLS excitation
57. Detail of a waveguide consisting of straight sections of length $d$ joined discontinuously