Del Grosso's [Acustica 24, 299-311 (1971)] formulation, which predicts the phase speed of propagating axisymmetric modes inside a liquid-filled tube, is here extended to the complex domain in order to predict the attenuation, as well as the sound speed, of the modes as a function of frequency. Measurements of the sound speeds and the attenuations of the modes were performed in a water-filled Poly (methyl methacrylate) (PMMA) tube of internal radius, b=4.445 cm, in the range of the wavenumber-radius product, k(1)b, from 2 to 10. Parts of three or four modes were investigated and the measured sound speeds and the damping of the modes were compared with the theoretical predictions. The theory was then used to estimate the modal sound speeds and attenuations in a stainless-steel pipe filled with mercury having the same dimensions as are used in the Spallation Neutron Source at Oak Ridge National Laboratory, Tennessee.

The most popular technique for estimating the gas bubble size distribution (BSD) in liquids is through the inversion of measured attenuation and/or sound speed of a travelling wave. The model inherent in such inversions never exactly matches the conditions of the measurement, and the size of the resulting error (which could well be small in quasi-free field conditions) cannot be quantified if only a free field code exists. Users may be unaware of errors because, with sufficient regularization, such inversions can always be made to produce an answer, the accuracy of which is unknown unless independent (e.g. optical) measurements are made. This study was commissioned to assess the size of this error for the mercury-filled steel pipelines of the target test facility (TTF) of the spallation neutron source at Oak Ridge National Laboratory, TN, USA. Large errors in estimating the BSD (greater than 1000% overcounts/undercounts) are predicted. A new inversion technique appropriate for pipelines such as TTF gives good BSD estimations if the frequency range is sufficiently broad. However, it also shows that implementation of the planned reduction in frequency bandwidth for the TTF bubble sensor would make even this inversion insufficient to obtain an accurate BSD in TTF.

This paper uses a finite element method (FEM) to compare predictions of the attenuation and sound speeds of acoustic modes in a fluid-filled pipe with those of the analytical model presented in the first paper in this series. It explains why, when the predictions of the earlier paper were compared with experimental data from a water-filled PMMA pipe, the uncertainties and agreement for attenuation data were worse than those for sound speed data. Having validated the FEM approach in this way, the versatility of FEM is thereafter demonstrated by modeling two practical applications which are beyond the analysis of the earlier paper. These applications model propagation in the mercury-filled steel pipework of the Spallation Neutron Source at the Oak Ridge National Laboratory (Tennessee), and in a long-standing design for acoustic sensors for use on planetary probes. The results show that strong coupling between the fluid and the solid walls means that erroneous interpretations are made of the data if they assume that the sound speed and attenuation in the fluid in the pipe are the same as those that would be measured in an infinite volume of identical fluid, assumptions which are common when such data have previously been interpreted.

This paper describes a demonstration and explanation of sound absorption in water due to bubbles, and in air due to a fog of water droplets. It is suitable for 10-12 year olds, but the paper indicates where further exploration of the simplifications in the explanations provided for that age range would allow the demonstration to be used for undergraduate and Masters-level teaching. Applications to submarines, the space shuttle, and neutron generators are described. The demonstration is designed for transportation in a family-sized car.

Equations for the nonaxisymmetric modes that are axially and circumferentially propagating in a liquid-filled tube with elastic walls surrounded by air/vacuum are presented using exact elasticity theory. Dispersion curves for the axially propagating modes are obtained and verified through comparison with measurements. The resulting theory is applied to the circumferential modes, and the pressures and the stresses in the liquid-filled pipe are calculated under external forced oscillation by an acoustic source. This provides the theoretical foundation for the narrow band acoustic bubble detector that was subsequently deployed at the Target Test Facility (TTF) of the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL), TN.