Propagation and reflection of low frequency sound in single and coupled pairs of straight and curved ducts is investigated with and without flow of the propagating medium. The work is divided into three sections.

The first section deals with general propagation theory in straight and curved radial ducts of rectangular cross section with and without uniform flow. The effects of flow on the propagation of energy and the cut-off frequencies of higher modes are investigated experimentally and theoretically. A theoretical explanation in terms of wave number of why the cut-off frequency is independent of direction of propagation of sound relative to the flow is presented. The behaviour of phase velocity and group velocity near cut-on is also considered.

Sound propagation in radial bends of rectangular cross section is investigated using two methods, the first of which utilizes the traditional solution of the wave equation in cylindrical co-ordinates. An iterative method of solution of the characteristic equation is discussed and used to predict the acoustic pressure and particle velocity distributions of two propagating modes. Comparison is made with experimental results and the results of other workers. Good agreement is obtained. The theoretical investigation using cylindrical co-ordinates is limited to the case without flow.

An approximate method of analysis of low frequency sound in radial bends is developed using conformal mapping techniques. As well as overcoming the need to evaluate complicated expressions of Bessel and Neumann functions, this approach allows theoretical consideration of the effects of flow. Simple equations are developed which predict the angular wave numbers of the (0,0) mode and higher evanescent modes as well as the cut-off frequencies of higher modes with and without flow. The results of the analysis agree with results obtained by other workers using cylindrical co-ordinates solution. The effects of flow on the pressure distribution and cut-off frequencies of higher modes are considered.

The second part of the thesis is concerned with sound generation and propagation in duct systems. Sound generated in a rectangular straight duct with rigid walls by a dipole piston source is theoretically investigated. The pistons are of equal area and fill the cross section of the duct. The characteristic impedance and radiation efficiency of the source is investigated for varying phase angle between pistons. The source is shown to be an extremely good radiator of sound when the pistons are in phase and to radiate no sound power at all below the cut- off frequency of the first cross mode of the duct when the pistons are π radians out of phase.

The effects of a curved axial partition on the impedance of a curved bend are investigated theoretically and experimentally. Whereas previous investigations have established that a curved bend provides negligible discontinuity to acoustic propagation, the presence of a central partition is found to drastically modify the propagational characteristics of the bend resulting in high reflection of sound at a number of discrete frequencies. By contrast, presence of a central partition in a straight duct would have no effect at all below the cut-off frequency for the first cross mode of the duct.

The third part of the work deals with the development and testing of two reactive attenuators, based upon a principle mentioned by Rayleigh (Theory of Sound, Vol. II, p.63) and attributed to Herschel. Sound propagation in a single duct is caused to split into two parts which travel along separate parallel ducts and when recombined produce non-propagating modes. The sound is thus reflected and the device becomes an effective attenuator in prescribed frequencies. Such attenuators might be used for rigid walled ducts.

The first attenuator is designed to fit into a 90 degree bend in a rectangular duct system and relies on a center body to create an impedance mismatch at the attenuator exit. The center body is shaped to provide a low pressure drop across the device. performance of the attenuator is theoretically analysed with and without flow. The analysis allows the redesign of the configuration of the attenuator to optimize its performance. An optimum attenuator is developed which provides a transmission loss of at least 10 dB over three quarters of an octave and losses of 30 to 50 dB at a number of discrete frequencies in the three quarters octave frequency range.

Flow is found to substantially reduce the high attenuation obtained at the discrete frequencies but a transmission loss of 10 dB is still obtained over three quarters of an octave for a flow rate of M=0.08 in the upstream straight duct. The effects of flow on the design frequency and the pressure reflection coefficient are quantified.

The second attenuator is designed for use in straight ducts of circular cross section and relies on an acoustic delay line to generate a series of evanescent modes and a resultant impedance mismatch at the device exit. The attenuator is investigated experimentally with and without flow for speeds up to M = 0.37. The device is shown to provide higher levels of attenuation and a 10 dB rejection band over an octave for the case without flow. The dis- turbance to the fluid flow in the main duct is negligible. A theoretical analysis of the delay line attenuator over its operating frequency range is not attempted. However, it may be theoretically described for the very low frequency portion of its range using a lumped circuit analysis. The theory predicts reasonably well the positions of the amplification of sound, measured in the very low frequency range.