Nonspecular Reflection Research Articles

Ray models for sound propagation and attenuation in ducts, in the absence of mean flow

Ray models are constructed for describing the sound fields in lined, two dimensional ducts due, respectively, to a point source and a line source. Corrections for non-specular reflection and for multiple reflection are included. Fields calculated by using the models are compared with the corresponding exact fields. The results show that very reasonable accuracy can be obtained (especially when the appropriate corrections are included in the model) from such models when used to describe the sound field in a duct up to at least distances of the order of three duct widths from the source. Thus, it is concluded that for many applications in duct acoustics, ray models are sufficiently accurate and preferable in use to mode models because of the possible savings in computation time. Also they can provide a clearer, more direct picture of the physics of the interfering waves making up the sound field.

Some Effects of Multiple Scattering on the Distribution of Solar Radiation in Snow and Ice

AbstractMultiple scattering of the solar flux in snow and “bubbly” ice can account for the variable albedo, the non-specular reflection, the non-exponential flux decrease near the surface, and the large upward flux within the medium. The scattering problem has been formulated and solved exactly, assuming isotropic scattering in a plane-parallel, semi-infinite, grey medium. The solution shows a non-exponential flux decrease near the surface and an exponential decrease deep in the medium. For such a medium, the albedo will increase with decreasing solar altitude in a manner which agrees to within one per cent of observed snow albedos in the Antarctic.

Some Effects of Multiple Scattering on the Distribution of Solar Radiation in Snow and Ice

AbstractMultiple scattering of the solar flux in snow and “bubbly” ice can account for the variable albedo, the non-specular reflection, the non-exponential flux decrease near the surface, and the large upward flux within the medium. The scattering problem has been formulated and solved exactly, assuming isotropic scattering in a plane-parallel, semi-infinite, grey medium. The solution shows a non-exponential flux decrease near the surface and an exponential decrease deep in the medium. For such a medium, the albedo will increase with decreasing solar altitude in a manner which agrees to within one per cent of observed snow albedos in the Antarctic.

RECONSTRUCTION OF SUBGLACIAL RELIEF FROM RADIO ECHO SOUNDING RECORDS

In 1967 a party from the Scott Polar Research Institute, Cambridge, England, carried out a radio echo sounding survey of the Antarctic ice sheet; their data have been used in the analyses discussed. The radio echo sounding apparatus, basically a pulse‐modulated radar operating at 35 Mhz, was installed in a U.S. Navy Constellation aircraft with the aerials attached to the tail, giving a fan‐shaped beam. The beam is broadest along the line of flight, causing problems of interpretation analogous with those encountered in marine echo sounding and seismic surveying. Also, bottom echoes are affected by refraction at the ice surface. Examples of hyperbolic variations of echo delay with horizontal movement may be seen at the edges of ice shelves, crevasses, or cracks at the bottom of the ice. Sometimes more complex surfaces can give roughly hyperbolic echo profiles. It is possible to distinguish specular from nonspecular reflections; we use a method of computing the position of specular reflecting points from the echo profile which allows the shape of the reflecting surface to be calculated. A computer program transforms the digitized film record into a real space profile. Errors may arise from faulty digitization, but these have been largely eliminated by checking the digitized points early in the program. Occasionally, because of their similar range and echo strength, strong side echoes may be confused with sub‐ice features. A cross‐section of Nimrod Glacier and the bottom of the ice sheet near Vostok have been plotted; in both cases there is a striking difference between the computed space profile and the echo profile.

Electron Scattering at a Rough Surface

The lifetime of electrons in a skipping trajectory is limited by an occasional diffuse-surface-scattering event that removes the electron from a given quantum energy level. For elastic transitions between surface states, the scattering rate ${\ensuremath{\Gamma}}_{s}$ is predicted to become larger with increasing magnetic field as ${H}^{2}$. Such increasingly nonspecular surface reflection has been observed in a series of Ga and Sn samples with deliberate and controlled surface roughness.

Bottom Reverberation for 530- and 1030-cps Sound in Deep Water

Bottom reverberation measurements were made during September, 1954, with 530- and 1030-cps sound in 2100 fathom water near San Diego for ping durations of 0.1, 0.25, 0.5, 1.0, and 2.0 sec with omnidirectional sources and receivers. The data were analyzed by assuming that the returned sound consisted of both specularly and nonspecularly reflected sound, analogous to the regular and diffuse reflected light from Bristol board. At normal incidence the losses on reflection for the 530- and 1030-cps sound were 19.5±2.5 db and 15.4±1.7 db, respectively. The other sound returning from the bottom as reverberation was assumed to be due to nonspecular reflections obeying Lambert's law of diffuse reflection. The reverberation level due to the nonspecular reflections was then analyzed to obtain the scattering constant μ of the bottom. A value of 10 logμ=−27 db was obtained for both the 530- and 1030-cps sound. The curves computed for a sine squared dependence fit the data for grazing angles from 90° to 30°. A comparison with published values of other investigators indicates that for clays, muds, or fine grained sands there appears to be no significant frequency dependence over a range of seven octaves.

Problems in the Determination of Contours of Solar Lines Near the Extreme Limb

In the first part of the paper the distorting effects of the Earth's atmosphere on the distribution of light at the extreme limb of the Sun are considered. An analytical expression is found which describes the resultant redistribution of light in the focal plane of the telescope; the effects of “seeing” are represented by a Gaussian term, particle scattering and non-specular reflection by the telescope optics are included in a power-law term. This redistribution function forms the kernel of the integral equation relating the true and observed intensities at any point. A geometrical idealization reduces the two-dimensional equation to an equation in one dimension. Methods of solving this equation which do not presuppose an analytical form of the true distribution are investigated and it is shown that the solutions must be regarded as discontinuous. In order to apply these methods, observations of the K line of Ca II were made at points within |$\pm 10$| ″ arc of the limb, on two days. The relevant parameters in the redistribution function were determined from the observations. A numerical application of the solution of the integral equation then gave the true line profiles. The accuracy attainable in the solution is shown to depend rather strongly on the width of the kernel and hence on the atmospheric conditions.

Nonspecular Reflection of Sound by Finite Plates and Shells in Liquids

Results are given of a detailed theoretical and experimental investigation of the nonspecular reflection (N.R.) of sound by thin plates resulting from flexural waves, as well as of a new type of N.R., resulting from longitudinal waves in a thin plate, and the phenomenon of N.R. in cylindrical shells and thick plates found by the author. It is shown that during N.R. an effect of coincidence resonance takes place. The fine structure of N.R. due to coincidence resonance has been experimentally observed and investigated. It is shown that N.R. takes place also in case of scattering of sound by finite thin cylindrical shells and thick plates. The peculiarities of N.R. in the above-mentioned cases are stated. It is shown that if the radius of the cylindrical shell is substantially greater than the wavelength of sound in liquid, the direction of N.R. from a shell coincides with the direction of N.R. from a plate of the same thickness and material. It is shown further that in case of a thick plate the number of maximums of N.R. at great thicknesses and high frequencies of vibrations is very high and decreases with the decrease of frequence. In limiting cases only two N.R. (thin plate) are observed. The N.R. in thick plates is shown to be due to the propagation of the so-called normal waves in the plate considered as an elastic layer of finite thickness.

Radio reflections from aurorae

The paper offers an interpretation of auroral echoes observed at Jodrell Bank on two occasions in 1953. It is concluded that in each case the echoes are due to direct, non-specular reflection from an auroral arc extending more than 1000 km along a parallel of geomagnetic latitude. The reflection apparently occurs in a region of the arc of limited vertical extent at a height of about 125 km. The observed line of sight velocities of intense reflecting centres are interpreted as true motions along the arc with velocities of the order of 1–2 km sec −1.

On the Nonspecular Reflection of Electromagnetic Waves

The nonspecular reflection of plane electromagnetic waves of arbitrary polarization by certain perfectly conducting surfaces composed of either semicylindrical or hemispherical bosses on an infinite plane is analyzed. Solutions for the problem of the single boss on an infinite plane and a plane wave at an arbitrary angle of incidence are given and extended subject to the single-scattering hypothesis to obtain the far field solutions for certain small finite patterned distributions and both small finite and infinite uniform random distributions of bosses small compared with the wavelength. The results for the various cases are then compared in the plane of incidence and similarities between the analogous expressions for the distributions of semi-cylinders and hemispheres are noted. Expressions are obtained for the ratios of the components of the reflected intensity and radial energy flux polarized parallel and perpendicular to the plane of incidence as well as for the total intensity and radial energy flux for the case where the incident wave is unpolarized. It is found that for certain values of the parameters the reflected radiation may consist only of either the specular or the scattered contributions, while for other values one of the scattered contributions, either the parallel or perpendicular component, may vanish. The results also indicate the occurrence of an extremum in the reflected radiation in the vicinity of the specular angle of reflection, which for certain ranges of the parameters for the small finite distributions may be a minimum rather than a maximum. For these cases there is also some critical angle of incidence (not necessarily π/2 or grazing incidence) for which the reflection at the specular angle is completely specular. The analogous distributions of cylinders and spheres are also considered.

On the Nonspecular Reflection of Sound from Planes with Absorbent Bosses

The nonspecular reflection of plane waves of sound from certain surfaces composed of absorbent bosses (semicylinders or hemispheres of arbitrary impedance) on an infinite plane of ∞ or 0 impedance is considered. Exact solutions are obtained for the problem of the single boss and then extended, subject to the single-scattering hypothesis, to obtain far field solutions for certain planar distributions of bosses of radii small compared with the wavelength. The results are compared with those obtained previously for non-absorbent bosses, and it is shown that the effects of the finite impedance are most pronounced in the simple source terms of the scattered components and may lead to either a decrease or an increase in the radiation reflected at the specular angle. Another effect of the finite impedance (for the small finite distributions) is to shift the critical value of the angle of incidence for which the reflection at the specular angle consists only of the specular component—below this value the reflection at the specular angle being a minimum and above it a maximum. For the infinite uniform random distributions it is found that the effect of the bosses is essentially but to change the impedance of the plane—these effective impedances being functions of the angle of incidence and the parameters and distribution of the bosses. The effect of the finite impedance of the bosses is most pronounced for these distributions yielding terms much lager than those previously retained for the nonabsorbent bosses. The results for the analogous distributions of cylinders and spheres are also given.

On the Non-Specular Reflection of Plane Waves of Sound

The non-specular or scattered reflection of plane waves of sound by various rigid, non-absorbent non-porous surfaces composed of either semicylindrical or hemispherical bosses (protuberances) on an infinite plane is analyzed. Exact solutions for the problem of the single boss and a plane wave at an arbitrary angle of incidence are derived through consideration of a cylinder or sphere and two simultaneously incident “image waves.” Finite patterned distributions of such bosses are then treated and the far field solution obtained subject to the restriction that the secondary excitations of the various bosses be neglected. (The equivalent problems for cylinders and spheres are also considered as well as the second-order solution, for the cylindrical case, which takes into account the interaction of neighboring elements.) These solutions are found to contain the characteristic Fraunhofer terms for a grating or lattice. The asymptotic solutions for the single bosses (Kr≫1, Ka<1) are then extended to consider both finite and infinite uniform random distributions. The solutions for the finite distributions are found to contain the characteristic Fraunhofer terms for similarly shaped apertures. The solutions for the infinite distributions (of semicylinders or hemispheres) are found to be remarkably similar when expressed in terms of the volumetric departure from the plane per cm2 of distribution. Some extensions and ramifications of the results are also considered.

Reflection of Sound From Submerged Plates

It has been found that an appreciable reflection occurs in the direction of the incident wave when high frequency underwater sound strikes a submerged steel plate at an oblique angle of incidence. The magnitude of this “non-specular” reflection, together with the associated transverse vibrations in the plate, has been studied experimentally as a function of frequency, plate dimensions and angle of incidence. Significant non-specular reflection occurs from bounded plates between about one-quarter inch and two inches thick, when the product of thickness in inches and frequency in kilocycles per second lies between about 20 and 60 in.-kc. Within this range, the angle of incidence for maximum non-specular reflection, η is described by the empirical relation: sinη = 2.16/(bf)13. This relation has been found to apply also to 0.002 inch plates at 15 megacycles. The results of the present study are in agreement with a theoretical analysis by Fay, and with the experimental results obtained by Sanders at frequencies of several megacycles.

Experimental Investigation of Non-Specular Reflection of Sound from Submerged Steel Plates

It has been found that an appreciable reflection occurs in the direction of the incident wave when high frequency underwater sound strikes a submerged steel plate at an oblique angle of incidence. The magnitude of this “non-specular” reflection, together with the associated transverse vibrations in the plate, has been studied experimentally as a function of frequency, plate dimensions, and angle of incidence. Significant non-specular reflection occurs from bounded plates between about one-quarter inch and two inches thick, when the product of thickness in inches and frequency in kilocycles per second lies between about 20 and 60 in-kc. Within this range, the angle of incidence for maximum non-specular reflection, n, is described by the empirical relation sinn = 2.16/((fb)13), where b is plate thickness in inches and f is frequency in kilocycles. The results of the present study are in excellent agreement with a theoretical analysis by Fay, which includes plate displacements due to shear strain as well as those due to bending. The results do not agree with an analysis which neglects displacements of the plate due to shear strain.

Interaction between a Plate and a Sound Field in a Fluid Medium

When underwater sound impinges on a steel plate at an oblique angle of incidence, there have been observed strong reflections directed toward the source. An analysis of the interchange of energy between a sound field in a liquid medium and flexural vibrations in a plate immersed in the field indicates the mechanism involved in this type of non-specular reflection. It has been found that for a plate and a liquid of specified properties, the behavior of the system depends on the product of plate thickness and frequency. For a steel plate b inches thick in water at a frequency of f kilocycles per second, the forces exerted by the water on the plate become negligible for values of bf exceeding about 20. For values of bf less than about unity, the effect of the plate in the sound field becomes negligible. It is therefore in the range of values between 1 and 20 for which the results are of particular interest. The velocity of phase propagation and the attenuation of flexural waves having origin in the plate have been calculated as a function of bf. There has also been found the angle between the plate and the wave fronts generated in the liquid. This angle, for the upper range of bf, is substantially equal to the angle of incidence for maximum non-specular reflection. The calculated values are in good agreement with measurements made by W. J. Finney.