@article{franzoni_bliss_1998, title={A discussion of modal uncoupling and an approximate closed-form solution for weakly coupled systems with application to acoustics}, volume={103}, ISSN={["0001-4966"]}, DOI={10.1121/1.421344}, abstractNote={Modal analysis is often used to solve problems in acoustics, leading to a system of coupled equations for the modal amplitudes. A common practice in analytical work utilizing modal analysis has been to assume that weak modal coupling is negligible, thereby enabling the modal coefficients to be solved independently in closed form. The validity of this assumption, as well as the order of the error from neglecting modal coupling, is discussed. It is possible to incorporate the principal effects of weak modal coupling in a very simple way without solving the fully coupled system. An approximate closed-form solution for weakly coupled systems of equations is developed. The procedure gives insight into the errors incurred when coupling is neglected, and shows that these errors may be unacceptably large in systems of practical interest. A model problem involving a pipe with an impedance boundary condition is solved when the one-dimensional sound field is harmonically driven, and when it undergoes reverberant decay from initial conditions. The approximate solution derived in this paper is compared with results for the fully coupled and fully uncoupled equivalent problems. The approximation works well even for systems where the coupling is fairly strong. The results show that modal coupling must be included, at least approximately, if certain salient features of the sound field, such as intensity flow and detailed reverberant structure, are to be predicted correctly.}, number={4}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={Franzoni, LP and Bliss, DB}, year={1998}, month={Apr}, pages={1923–1932} }
 @article{franzoni_elliott_1998, title={An innovative design of a probe-tube attachment for a microphone}, volume={104}, ISSN={["0001-4966"]}, DOI={10.1121/1.423873}, abstractNote={Nonintrusive devices are needed to measure sound pressure levels in the mid- to high-frequency range. This need arises due to the small acoustic wavelengths which are present at these frequencies, and the interference caused by conventional microphones which are typically of relatively large diameter. Smaller microphones are less sensitive, and may not be small enough to be useful at very high frequencies or when physical size constraints are limiting. Simple probe attachments have been developed by others to address these problems; however, generally the transfer functions of these devices have possessed undesirable peaks due to the presence of standing waves within the transducers. In this paper, several possible options for making a microphone attachment that will convert a standard 12-in.-diam microphone into a probe-tube are discussed. Recommendations are made with regard to the particular use and ease of construction of the attachment. The new concepts eliminate standing waves, within certain frequency bands that are controlled by the geometry of the attachment, without the addition of damping material in the sound path.}, number={5}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={Franzoni, LP and Elliott, CM}, year={1998}, month={Nov}, pages={2903–2910} }