The Acoustics of Pipe Arrays

Abstract

Summary A theoretical analysis is given for the acoustical behaviour of the pipemicrobarograph systems used to detect acoustic gravity waves and other modes of infrasound. It is shown how to compute the response of the microbarograph to a fluctuating pressure at any one inlet port of the pipe and how the results of such computations may be used to calculate the response to a plane sound wave traversing the system. The analysis is illustrated by numerical examples obtained by means of a computer program. These examples confirm that the tapered tube modelled after Daniels’ line microphone has very good characteristics, but that good results may also be obtained using pipes of uniform bore. The work leans heavily on Benade’s calculations of sound propagation in a circular conduit. For the purpose of observing acoustic-gravity waves and other rapidly progating modes of infrasound (of period 1-1000 s) it is common practice to enhance the signal-to-noise ratio by attaching a pipe to the microbarograph. This pipe is often several hundred feet in length and perforated by small inlet ports spaced at intervals of a few feet along its length. At a given frequency the disturbances entering the various ports are added acoustically in the pipe and transmitted rapidly along the pipe to the microbarograph. The noise, mainly atmospheric turbulence advected with the wind, is partially incoherent at the different inlets, and moreover travels slowly compared with the acoustic signals we are trying to observe and slowly compared with the speed of sound inside the pipe. Thus the contributions from the fast-moving signals, at least at low frequencies, tend to be added in phase at the microbarograph whereas the contributions from the noise do not. Daniels (1949) suggested the use of a tapered pipe narrowing in steps toward the end far from the microbarograph. The acoustic impedance of an inlet was carefully matched to the change in characteristic impedance of the pipe at that inlet in such a way that waves travelling away from the microbarograph in the pipe were not reflected. It was realized, however, that in order for the pipe to act properly as an array many inlets were required, far more than a convenient number of steps in the pipe radius. Moreover, only certain gauges of pipe were available, so that considerable compromise was required in order to use Daniels’ design in the field. On top of this, when practical dimensions for pipes are taken into account it is found that at the frequencies of interest in geoacoustics the narrow tube approximation is more applicable than Daniels’ theory which, with its assumed high velocity of sound in the pipe, agrees more with the wide tube approximation. These considerations lead one to speculate on the true acoustic behaviour of the