Search

An inhomogeneous plane wave, i.e., one having an exponential decay across the wavefront, may be used to model the sound incident on any reflecting boundary. If the decay is away from the boundary there is normally an element of reflection gain associated with the process, corresponding to a release of previously stored energy. This gain is in addition to the loss expected for an equivalent homogeneous wave. It is shown that the gain element is equal to the exponential decay in the inhomogeneous wave resolved across the horizontal beam displacement. This result holds very generally for transmission as well as reflection, for change of wave type, and for the gain element occurring when the incidence medium is lossy. In application to guided waves these results automatically ensure that the attenuation rate is the same, whether modeled by inhomogeneous waves with an element of gain, or by waves with a beam displacement. The incident inhomogeneous wave may be decomposed into a spectrum of homogeneous plane waves having a spread in angle. Similarly an attenuating mode may be regarded as propagating with a spread in equivalent ray angles. [ABSTRACT FROM AUTHOR]

Recent results showing the equivalence of mode attenuation per cycle and reflection loss of the equivalent ray did not hold in shallow water with a small number of modes. The failure is demonstrated to be linked to the concept and definition of a mode cycle distance for low mode density. Attenuation rates of modes and average attenuation rates of rays are now shown to be equal for all mode densities, provided the attenuation is not too large and the ray cycle distance is taken as the sum of the geometrically traced ray distance and the boundary beam displacement. [ABSTRACT FROM AUTHOR]

A concise energy-flux formulation is used to investigate the range- averaged acoustic propagation in ocean ducts. Examples treated have isovelocity, linear, and parabolic sound speed profiles. The results are expressed as the product of a scale factor and, for the latter two examples, a depth factor. The scale factor has a similar form in each case, and remains simple and easy to use even when the profile is asymmetrical and the parameters vary with range. The appropriate solution for transmission from an isovelocity duct to a duct of arbitrary profile is also given. Surprisingly, the depth factor generally has a nominal infinity when receiver depth equals source depth in an unchanging but stratified duct, or when velocity at the receiver equals that at the source, or for scaled depths in a range-dependent duct. These infinites are discussed from the flux, ray, and mode viewpoints and a ray-tracing demonstration is provided. For the special case of axial source and receiver, the character of the infinite is different, and an important point is that it occurs only for velocity minima sharper than that of the parabolic profile. The latter profile has in several respects a critical nature. [ABSTRACT FROM AUTHOR]

Even in isovelocity water the wave or modal nature of the sound propagation causes special effects at four particular depths. Thus, the range-averaged level shows a zero at the free surface, a maximum at the source depth, and effects of uncertain sign at the bottom and near the source complementary depth. These peaks show further curious behavior, akin to interference, as source depth is varied. The present source depth peaking is a wave effect in isovelocity water, in contrast with the flux-theory infinities predicted for refracting conditions. For large numbers of modes, the present source depth peak is normally 50% above the average, and this anticipates a similar wave-theory result for refracting conditions. [ABSTRACT FROM AUTHOR]

The formal energy-flux solution for range-averaged level in a varying duct depends on the definition of transmission loss, on the local impedances, and in a complicated way on the vertical angles and cross-track variations. But for most purposes a very simple low angle version is sufficiently accurate and well established to be virtually independent of the detailed profile. Surprisingly, the convergence factor with circular symmetry is also independent of the detailed profile; this is true for unbounded media as well. Depth transforms are presented for the angular distributions of intensity, initially without specific reference to sources. Angular distributions for discrete sources show some characteristic zeros and infinities. It is shown that only the Gaussian distribution is self-reproducing with changes in depth. The law of conjugate depths states that intensities will be equal at such depths, and it is expected that this law will be very robust. Work on these and allied energy-flux methods is reviewed. [ABSTRACT FROM AUTHOR]

Several theoretical results linking ray and normal-mode quantities are derived by assuming Wentzel-Kramers-Brillouin (WKB) solutions for the depth dependence of the acoustic field in both water and bottom. Some of the results are not new but are extended here to the general case of reflection from a structured, lossy bottom: (1) Mode and ray cycle distances are equal if the ray cycle distance includes the beam displacement on reflection; (2) cycle distance is simply related to the normalization of the normal modes; (3) mode attenuation per cycle is equal to bottom loss per bounce of the equivalent ray; (4) a complete normal-mode solution for water may be obtained from the plane-wave reflection coefficient with no further knowledge of the bottom; and (5) the WKB solution for the bottom is equivalent to a calculation assuming interfering geometric ray paths. [ABSTRACT FROM AUTHOR]

The loss on reflection of a homogeneous acoustic wave from the boundary of an absorbing fluid is derived in several ways, including a calculation based on the attenuation along the beam displacement. For a so-called inhomogeneous plane wave there is an extra term, and the overall effect can be a loss or a gain. The paper considers several approaches to mode attenuation in an isovelocity or Perkeris channel with a lossy lower medium. We compare the horizontal attenuation of a mode with the horizontal attenuation of a ray due to multiple reflection losses. For exact agreement at all angles it is necessary either to include the beam displacement in the cycle distance, or to use the reflection coefficient appropriate to inhomogeneous waves, but these latter provisos are important only for shallow water and modes near cutoff. Beam displacement plays a part in both the reflection loss and the cycle distance calculations, and these aspects may be generalized. [ABSTRACT FROM AUTHOR]

The leakage attenuation from a duct is simply related to the field level outside the duct, and the relation can be applied to the surface sound channel. High-frequency measurements over the Biscay Abyssal Plain support the predicted relation and indicate that the loss is mainly due to scattering at very shallow angles, presumably from the surface waves. Similarly low-frequency measurements in the same area show a diffraction loss occurring with effective angles that are again very shallow. Measurements by Reynolds and Pryce at 7.5 kHz are also shown to correspond very closely to low-angle scattering, ruling out any large contribution from entrained bubbles. In addition, it is possible to estimate the residual bulk absorption. But their results at 3.25 kHz show marked additional effects that are interpreted as wide-angle scattering and absorption due to small fish, and the existence of such deep-water fish attenuation is thought to be both novel and important. Use of our leakage relation has helped to identify and to disentangle five separate loss mechanisms. [ABSTRACT FROM AUTHOR]

The formation of sharp rays or beams in Wood's model shallow-water propagation experiments [V. M. Albers, Ed., Underwater Acoustics (Plenum Press, Inc., New York 1963), pp. 159-192] is due to an angular selection, and the resulting interference between neighboring high-order modes. Details of the interference mechanism are considered. A given beam should vanish and then re-form with a calculable characteristic distance. The distance is about 4 m in Wood's experiments, and the focusing is clearly visible in his results. These ideas are also applied to a moiré fringe analog, to shallow-water propagation, deep-water propagation, and to transmission of images in fiber optics. [ABSTRACT FROM AUTHOR]

Multiple acoustic scattering in line and plane arrays of spheres can sometimes reduce the acoustic pressure on the sphere surface to well below the free-field value, especially for gas-filled spheres in water. However, under certain conditions, there can be an enhancement. The resonance phenomenon is much sharper for a single spherical bubble than for a cylindrical bubble or a cylindrical vortex. The line array of small spheres behaves just like the cylindrical bubble: the sharp sphere resonance is suppressed and a broader resonance at a lower frequency appears. A plane array of such spheres behaves just like a plane screen of gas-there is no resonance at all. The reduction in phase velocity is calculated from scattering considerations for a composite medium having a low concentration of below-resonance spheres. [ABSTRACT FROM AUTHOR]

In a correlation echo-ranging system, many features of any correlation loss may be predicted without considering detailed mechanisms. Correlation loss may be due to both a spreading time delay, τ and a spreading in Doppler-frequency shift [lowercase_phi_synonym]. First, these effects are considered separately, for one-way transmission and for two-way transmission or echo ranging. Generally, the total correlation loss may be regarded as due to a two-dimensional spreading in the τ-[lowercase_phi_synonym] plane. When τ and [lowercase_phi_synonym] spreading are both significant, the loss for an FM pulse is much less than that for a noise pulse. The excess of the two-way loss over the one-way loss may often be about 112 dB for an FM pulse and 3 dB for a noise pulse. [ABSTRACT FROM AUTHOR]

A moiré fringe analog of the normal modes of sound propagation in shallow water is described, in which interesting patterns are obtained both by direct visual observation and by photographic recording. These are analogs for the profiles of sound pressure as a function of range and depth in the underwater field due to a single-frequency source. Since phase is correctly represented, the interaction patterns due to the presence of considerable numbers of interfering modes may be investigated experimentally. This is important since mathematical analysis becomes difficult when there are more than two modes. There is a discussion of the characteristics of these patterns (including the formation of 'loops') and also of those obtained by A. B. Wood in his sound propagation model experiments. [ABSTRACT FROM AUTHOR]

The different thermoviscous attenuation regions for the principal mode of sound propagation in a gas-filled tube may be defined in a simple diagram, with boundaries based on discriminants containing dimensionless combinations of radius, wavelength, and mean free path. The additional condition for propagation of higher-order modes may be placed on the same diagram. The condition is always satisfied in the ''very wide tube'' region, which makes experimental investigations of the principal mode more difficult in this region. [ABSTRACT FROM AUTHOR]

Sound propagation has been studied for several years in the shallow waters of the Bristol Channel. The measurements central to this account have involved repeated transmissions of a sequence of tone pulses, with frequency varying from 0.3 to 4.5 kHz, the arrivals building up into a simple display. The signals were transmitted and monitored by fixed bottom-laid transducers, with path lengths up to 137 km. The investigations have been supported by other time-series measurements: in long-range echo ranging on fish and other reverberators, in ambient noise, and in oceanography. As a result of prolonged detective work, 11 different mechanisms causing signal fluctuation have been identified, eight of which would not have been revealed in the absence of long time-series results. Four reasons for the importance of long-term fixed-transducer multiple-frequency studies are given, as follows, each illustrated by one of the fluctuation types: (a) Many effects need relatively long studies if they are to be seen at all, e.g., the diurnally changing attenuation due to fish. (b) Some effects may only be understood by their behavior over long periods, e.g., fluctuations due to internal waves and their tidal dependence. (c) Some effects occur at random times, to be observed only by patient waiting, e.g., storms. (d) Understanding of the absolute transmission levels involves a knowledge of the variations in level, especially the variations with season. [ABSTRACT FROM AUTHOR]

For medium-to-long ranges in shallow water, and for frequencies above about 100 cps, energy is still present in at least the first two normal modes. The observed transmission laws cannot then be explained, as has been usual, by summing the normal modes with separate attenuations due to the boundary losses. The probable explanation is the presence of an enhanced body attenuation, possibly due to bladder fish. [ABSTRACT FROM AUTHOR]

A possible cause of the anomalously high deep-water acoustic attenuation in the region from 50 cps to 5 kcps is scattering and absorption by bathypelagic fish having swim bladders. But calculation shows that the members of batbypelagic fish are normally about two orders of magnitude too low so, although out the main cause, they might sometimes contribute significantly. In comparison, shallow-water attenuation shows important effects caused by fish. [ABSTRACT FROM AUTHOR]

Signal ambiguity in correlation echo-ranging may often be calculated by a correlation process on the envelopes of pulse intensity in a frequency-time diagram. The ambiguity for crossing noise ribbons depends only on the ribbon lengths and the angle of crossing. The mean ambiguity has the same value for crossing lines, and this is the key result of the paper. The ambiguity pattern for touching curved lines is similar to that for touching curved noise ribbons of a definite width. As an example the entire ambiguity diagrams for straight or slightly curved lines may be simply calculated, in both the narrow- and wide-bandwidth cases. Simple formulas are given for the Doppler tolerance and the behavior near Doppler invariance. [Hudson Laboratories of Columbia University Informal Documentation No. 78. Work supported by the U. S. Office of Naval Research.] [ABSTRACT FROM AUTHOR]

Multiple acoustic scattering in line and plane arrays of spheres can sometimes reduce the acoustic pressure on the sphere surfaces to well below the free-field value, especially for gas-filled spheres. However, at spacings near half a wavelength, there can be an enhancement. The resonance phenomenon is much sharper for a single spherical bubble than for a cylindrical bubble, a cylindrical vortex, a line of spheres, or a plane array of spheres. For finite arrays, the end or edge effects can be quantitatively described by additional geometrically spreading waves, but only when the above pressure reductions are small and only close to the edge. With high scattering, a modified edge wave must be used. [Hudson Laboratories of Columbia University Informal Documentation No. 79. Work supported by the U. S. Office of Naval Research.] [ABSTRACT FROM AUTHOR]

Recently, the writer described a moiré fringe analog for underwater sound modes. Now, attention is given to the work of Pohl and Shubnikov with moiré patterns from circular grids which are of possible use in underwater array design and underwater sound propagation investigations. [ABSTRACT FROM AUTHOR]