Showing papers in "Journal of Applied Physics in 1948"
TL;DR: In this paper, the physical limitations of omni-directional antennas are considered and the potentiality of a broad band width of an antenna with the maximum dimension of 2a has been shown.
Abstract: The physical limitations of omni‐directional antennas are considered. With the use of the spherical wave functions to describe the field, the directivity gain G and the Q of an unspecified antenna are calculated under idealized conditions. To obtain the optimum performance, three criteria are used, (1) maximum gain for a given complexity of the antenna structure, (2) minimum Q, (3) maximum ratio of G/Q. It is found that an antenna of which the maximum dimension is 2a has the potentiality of a broad band width provided that the gain is equal to or less than 4a/λ. To obtain a gain higher than this value, the Q of the antenna increases at an astronomical rate. The antenna which has potentially the broadest band width of all omni‐directional antennas is one which has a radiation pattern corresponding to that of an infinitesimally small dipole.
1,954 citations
TL;DR: It is found possible to define delay time and rise time in such a way that these quantities can be computed very simply from the Laplace system function of the network.
Abstract: When the transient response of a linear network to an applied unit step function consists of a monotonic rise to a final constant value, it is found possible to define delay time and rise time in such a way that these quantities can be computed very simply from the Laplace system function of the network. The usefulness of the new definitions is illustrated by applications to low pass, multi‐stage wideband amplifiers for which a number of general theorems are proved. In addition, an investigation of a certain class of two‐terminal interstage networks is made in an endeavor to find the network giving the highest possible gain—rise time quotient consistent with a monotonic transient response to a step function.
1,693 citations
Journal Article•
1,004 citations
TL;DR: In this article, a mathematical theory of this essentially new phenomenon is presented together with some of the experimental data that aided in the formulation and testing of the theory, which is separated into two phases: first, the formation of part of the metal liner into a long thin jet traveling longitudinally at very high velocities (30,000 ft/sec.) and, second, the forcing aside of the target material by the extremely high pressures (0.3m atmo...
Abstract: Explosives detonated in contact with thick steel plates produce much deeper holes in the steel when there is a cavity in the explosive in contact with the plate. While this phenomenon has been known for more than 150 years, the enormous increase in penetrating power that can be produced by lining the explosive cavity with thin metal has been discovered only recently. During the war a number of light, low velocity, antitank weapons (e.g., the rocket‐propelled Bazooka) were developed which made use of this phenomenon to perforate thick armor plate.A fairly complete mathematical theory of this essentially new phenomenon is presented together with some of the experimental data that aided in the formulation and testing of the theory. The process is separated into two phases: first, the formation of part of the metal liner into a long thin jet traveling longitudinally at very high velocities (30,000 ft./sec.) and, second, the forcing aside of the target material by the extremely high pressures (0.3‐million atmo...
582 citations
TL;DR: In this paper, a basic theory of slots in rectangular wave-guides is given, and detailed formulae for the reflection and transmission coefficients and for the voltage amplitude in the slot generated by a given incident wave are given.
Abstract: A basic theory of slots in rectangular wave‐guides is given. The analogy with a transmission line is developed and established, and detailed formulae for the reflection and transmission coefficients and for the ``voltage amplitude'' in the slot generated by a given incident wave are given. While the complete expressions for these quantities are quite complicated and involve the summation of infinite series, certain parts of the expressions are comparatively simple. In particular, the ``resistance'' or ``conductance'' of slots which are equivalent to series or shunt elements in a transmission line are given by fairly simple closed expressions. Guide‐to‐guide coupling by slots and slot arrays are also considered. A more detailed summary of the main results of the paper is given in Section 1.
453 citations
TL;DR: In this paper, the fracture strength of a cavity-nucleated fracture was derived from the theory of nucleation, and the negative pressure that gives one bubble (i.e., fracture) in t seconds was determined.
Abstract: A liquid subjected to negative pressure is metastable; vapor bubbles form spontaneously and grow until the pressure of the system rises to the equilibrium vapor pressure. The rate of bubble formation is calculated from the theory of nucleation, and the negative pressure pt that gives one bubble (i.e., fracture) in t seconds is determined. pt is very nearly independent of t, and is proportional to σ32 where σ is the surface tension. Subcooled liquids such as glass also are metastable under negative pressure; cracks form spontaneously and grow until the pressure rises to the equilibrium vapor pressure. Nucleation theory leads to an expression for the fracture stress of glass that is proportional to (E2σ3)¼ where E is the elastic modulus. The transition from high temperature cavity‐nucleated fracture to low temperature crack‐nucleated fracture is examined.Fracture strengths calculated from nucleation theory agree satisfactorily with the maximum experimental values, and are an order of magnitude smaller than ...
447 citations
TL;DR: In this article, a quantitative investigation of the intensity of scattered radiation in a series of native and regenerated cellulosic objects, including bacterial cellulose and fibers transformed into cellulose IV, is offered.
Abstract: A quantitative investigation of the intensity of scattered radiation in a series of native and regenerated cellulosic objects, including bacterial cellulose and fibers transformed into cellulose IV, is offered. The technique used involves the use of copper radiation monochromatized by reflection, specimens with randomized orientation of equal size and density, rotation of the plane film, and measurement of primary beam intensity by means of a device introduced by Goppel.The procedure of evaluation consists of measuring integrated intensities of the crystalline peaks and that of the diffuse background. After correction of the latter for radiation scattered by air and for the background components due to Compton radiation and thermal scattering, as derived from exposures of sugar crystals and diamond, the diffuse background is represented by a curve exhibiting a flat maximum.The height of this maximum was assumed to be a correct relative measure of the disordered portion and the total intensity of the coher...
372 citations
TL;DR: In this paper, it is pointed out that the problems posed by these models are equivalent to an important problem in mathematical statistics, namely, the distribution of the smallest value in samples of size n drawn from a population having some probability density function f(x).
Abstract: In recent years there has been an increasing interest in the development of statistical theories of strength. A main aim of these theories is to explain in a reasonable way such things as the dependence of the strength of specimens on their volume or length. In this paper it is pointed out that the problems posed by these models are equivalent to an important problem in mathematical statistics, namely, the distribution of the smallest value in samples of size n drawn from a population having some probability density function f(x). The calculations made by mathematical statisticians give a far more complete description of the results to be expected than do the estimates to be found up to now in the technical literature.
194 citations
TL;DR: In this paper, the authors give a theoretical solution to a plate containing two circular holes of equal size, where the parametric coefficients involved in the solution are adjusted so as to satisfy the boundary conditions at the edges of the holes.
Abstract: This note gives a theoretical solution to a plate containing two circular holes of equal size. The method of solution is to add to the given stress system a suitable biharmonic function which gives no stress at infinity. The parametric coefficients involved in the solution are adjusted so as to satisfy the boundary conditions at the edges of the holes. Bipolar coordinates are used in the solution, by means of which explicit expressions are obtained for the parametric coefficients. Three fundamental stress systems are discussed in some detail, namely, the all‐around tension case, the longitudinal tension case, and the transverse tension case. Formulas of the stress along the edges of holes are derived and, in particular, values of maximum stress are calculated. The limiting case in which the holes are tangential is also discussed.
167 citations
TL;DR: In this paper, it was shown that surface sealing is a major factor in controlling cavity formation, and is the factor most responsible for non-Froude scaling of cavity phenomena.
Abstract: High speed motion‐picture studies were made of the dependence of air‐water entry cavities on the relevant physical parameters—in particular, on the atmospheric pressure over the water surface. Experiments on the vertical entry of spheres ¼ in. to 1 in. in diameter, with entrance velocities between 15 ft./sec. and 100 ft./sec., and air pressures between 1/60 atmosphere and 3 atmospheres, show that surface sealing of the cavity is a major factor in controlling cavity formation, and is the factor most responsible for non‐Froude scaling of cavity phenomena. Surface sealing is a function chiefly of the atmospheric density and projectile velocity, although surface tension is also important in its effect on splash formation. Froude's scaling is found to hold true in the region of low Froude's numbers and low atmospheric pressures. The measured average drag coefficient of the projectiles is independent of cavity size and shape. Jets are found to occur regularly and with great strength at both deep and surface closures of the cavity. The observed presence of jets in finite cavities is predicted by an extension of the Kirchhoff‐Helmholtz theory of the infinite (two‐dimensional) cavity to the case of finite cavities with finite cavitation numbers. Some of the results of this theory are mentioned.
153 citations
TL;DR: In this paper, a new theory of the formation of a discontinuous chip is presented, based on the friction angle τ between the chip and the face of the tool, by which the forces loading the machine tool steeply may be decreased.
Abstract: In this article values for the angles β and ν have been deduced (compare Fig. 3 and Eqs. (2) and (3)). New values have been deduced for the shear angle φ, Eqs. (16), (20), and (21). The increasing of the internal friction and the strain hardening have been considered.Equations for the work done in cutting per unit of length (6) and (13) have been deduced. For the cutting force Eqs. (14), (15), and (19) have been deduced. A high cutting speed decreases the friction angle τ between the chip and the face of the tool, by which the forces loading the machine tool steeply may be decreased. These forces are very highly dependent on the friction angle τ, since the rake angle α is negative.A new theory of the formation of a discontinuous chip is presented.
TL;DR: In this article, a simple and accurate method of determining pole figures by using a special sample mount with a Geiger counter x-ray diffraction goniometer is described and examples given.
Abstract: A simple and accurate method of determining pole figures by using a special sample mount with a Geiger counter x‐ray diffraction goniometer is described and examples given. Also, a correction formula is derived which takes into account absorption change and change in diffracting volume as the sample changes position with respect to the x‐ray beam.
TL;DR: In this paper, the equations for low amplitude space charge waves in an electron stream containing heavy positive ions are considered, and it is shown that at frequencies a little below the ion cyclotron frequency there should be a wave which increases in amplitude as it travels (negative attenuation).
Abstract: The equations for low amplitude space‐charge waves in an electron stream containing heavy positive ions are considered. At frequencies a little below the ion plasma frequency there should be a wave which increases in amplitude as it travels (negative attenuation). Ion motion tends to limit the rate of increase. In a beam filling a conducting cylinder and confined by a uniform magnetic field there should be an increasing wave at frequencies near the ion cyclotron frequency. Such waves might explain observed fluctuations in long electron beams.
TL;DR: It is shown that an optimum navigational ratio exists between that which leads to too slow an approach to the desired course and that which leading to instability.
Abstract: A graphical and mathematical analysis of homing and navigational courses of automatic target‐seeking devices is presented.Homing courses for a seeker‐to‐target speed ratio of over two are likely to be impractical for target interception.A method for obtaining a constant bearing course (navigational course) is developed. Some special cases of navigational courses have been studied graphically. It is shown that an optimum navigational ratio exists between that which leads to too slow an approach to the desired course and that which leads to instability.Graphical analysis of navigational courses for straight as well as circular target motion is also given.
TL;DR: In this article, it was shown that aluminum, magnesium, tungsten, and fused quartz are the only metals with a low attenuation loss for high frequency longitudinal and transverse sound waves.
Abstract: When high frequency longitudinal and transverse sound waves are sent through a multicrystalline rod of metal, attenuation losses result because of scattering and diffusion of sound waves by the grains. When the grain size is less than one‐third of the wave‐length, these losses are due to Rayleigh fourth power law scattering and are proportional to the grain volume. The scattering factor depends on the anisotropy of the elastic constants. Two different factors are obtained, one for shear waves and one for longitudinal waves. These factors have been evaluated for cubic and hexagonal metals. From the measured elastic constants the only metals with a low loss are aluminum, magnesium, and tungsten. The calculations indicate that the losses for aluminum and magnesium are about equal for longitudinal waves, but for shear waves magnesium has a very low shear loss. It has been found experimentally that magnesium has nearly as low a loss as fused quartz.Experiments with higher frequencies show that when the wave‐le...
TL;DR: In this article, a plane variable refractive index system can be transformed into a surface of revolution of constant refractive indices which reproduces the optical properties of the plane system, and the diameter of the feed circle can be made arbitrarily small by judicious use of an ellipsoidal reflector.
Abstract: The problem of devising a rapid scanning focusing antenna based on wave‐guide principles has been solved only approximately and not too satisfactorily. In the present paper, a known property of a plane optical system with variable index of refraction is shown to satisfy the requirements of such an antenna system. By a suitable transformation, the plane variable refractive index system can be transformed into a surface of revolution of constant refractive index which reproduces the optical properties of the plane system. This surface provides an apparently practicable solution to the scanning problem. It is shown that the diameter of the feed circle can be made arbitrarily small by judicious use of an ellipsoidal reflector.
TL;DR: In this paper, five methods are described for measuring the complex differential dynamic Young's modulus of rubber-like materials, under conditions of very small sinusoidal strain variations, at frequencies from 10−1 to 105 cycles per second and in a temperature range which at its widest limits extends from minus 60 to plus 100 degrees centigrade.
Abstract: Five methods are described for measuring the complex differential dynamic Young's modulus of rubber‐like materials, under conditions of very small sinusoidal strain variations, at frequencies from 10−1 to 105 cycles per second and in a temperature range which at its widest limits extends from minus 60 to plus 100 degrees centigrade. These methods are (1) measurement of the frequency of oscillation and the decrement of a ``rocking‐beam oscillator'' in which the restoring force is supplied by rubber (0.1 to 25 c.p.s.); (2) measurement of the frequency of resonance and the band width of a rubber reed which executes forced oscillation (10 to 500 c.p.s.); (3) measurement of the phase velocity and the attenuation of longitudinal waves in a thin rubber strip in the absence of standing waves (1 to 40 Kc); (4) measurement of the frequency of longitudinal‐wave resonance and the band‐width of a half‐wave transmission line (below 300 c.p.s.); (5) measurement of the change in the frequency of resonance and the change in the band width of a magnetostrictive rod against whose end a rubber sample is pressed (12 to 120 Kc). Equations are developed for calculating the complex modulus from the results of each experiment, and the practical advantages and limitations of the methods are described.
TL;DR: In this article, the authors determined the drag coefficients for ¼-inch to 1½-inch steel spheres shot into water vertically with speeds from 25 to 208 ft/sec.
Abstract: Drag coefficients have been determined from high speed motion pictures for ¼‐inch to 1½‐inch steel spheres shot into water vertically with speeds from 25 to 208 ft./sec. These drag coefficients correspond to the entrance cavity phase and to the v‐squared‐law drag forces only, the immediate effects on the spheres of other forces being eliminated in the calculations. It is found that CD is a function of both the Reynolds and Froude Numbers. Within the range investigated, the dependence may be expressed by CD=0.0174 ln(RF½).
TL;DR: The coefficient of heat transfer from a rotating disk to ambient air in case of a laminar boundary layer is theoretically calculated on the basis of von Karman's calculation of flow conditions as mentioned in this paper.
Abstract: The coefficient of heat transfer from a rotating disk to ambient air in case of a laminar boundary layer is theoretically calculated on the basis of von Karman's calculation of flow conditions.
TL;DR: In this article, the entropy and energy of deformation of a strained elastomer were analyzed in terms of observable quantities, including the volume effects caused by changes in mean pressure and crystallinity, and the effects associated with change in shape are sharply separated from those associated with changes in volume.
Abstract: The thermodynamic functions of principal interest in a strained elastomer are the entropy and energy of deformation. The volume is of secondary importance, and it can be assumed, with sufficient accuracy for most purposes, that the volume is linear in the temperature and the mean pressure. The basic partial differential equations of thermodynamics can then be integrated, yielding expressions for the energy and entropy of deformation in terms of observable quantities.In the present analysis the volume effects caused by changes in mean pressure and crystallinity are taken into account, and the effects associated with change in shape are sharply separated from those associated with change in volume. It is shown that the superelastic functions of deformation previously published (M. Mooney, J. App. Phys. 11, 582–92 (1940)) have a very general validity.
TL;DR: In this article, it was shown that the grain boundary slip in alpha-brass is a diffusion process and the diffusion mechanism is similar to the volume diffusion in alpha•brass.
Abstract: The viscous behavior of the grain boundaries in 70–30 alpha‐brass was demonstrated by anelastic measurements. It was shown that the grain boundaries cannot sustain permanently a shear stress and have a coefficient of viscosity decreasing with an increase of temperature. Using the same alpha‐brass specimen, the activation energy associated with the stress‐induced preferential orientation of pairs of zinc atoms in alpha‐brass (which is a diffusion process) was determined. This activation energy was found to be identical, within experimental error, to the activation energy associated with the grain boundary slip in alpha‐brass. This finding indicates that the grain boundary slip in alpha‐brass is a diffusion process and the diffusion mechanism is similar to the volume diffusion in alpha‐brass.
TL;DR: In this paper, the mass photoelectric absorption coefficient τ/ρ and the mass scattering coefficient σ/ρ of any element may be represented by a simple expression, and the calculated values of the calculated mass absorption coefficients μ/ρ are given for wave lengths from 0.01 to 40 angstroms for hydrogen and carbon and from λK to λL for aluminum, copper, tin, and lead.
Abstract: Evidence presented indicates that the absorption of quanta as defined by the mass photoelectric absorption coefficient τ/ρ and the mass scattering coefficient σ/ρ of any element may be represented by a simple expression.Tabulated values of the calculated mass absorption coefficients μ/ρ are given for wave‐lengths from 0.01 to 40 angstroms for hydrogen and carbon and from 0.01 to λK and λK to λL for aluminum, copper, tin, and lead. Graphs are given showing agreement with observed values.
TL;DR: In this paper, a method for the evaporation of alloys in high vacuum was developed, which from the nature of the procedure used should be applicable to all alloys which are not refractory.
Abstract: We have developed a method for the evaporation of alloys in high vacuum which from the nature of the procedure used should be applicable to all alloys which are not refractory. The method has been tested on α‐brass and β‐brass and on a gold‐cadmium alloy. These alloys have components whose vapor pressures are very different and yet chemical and electron diffraction analyses on the evaporated brass alloys and chemical analysis on the evaporated cadmium‐gold alloy show that the composition of the original alloy is held to within close limits.
TL;DR: In this paper, the electric field measured inside a stable non-precipitating cloud is less than 10 volts/cm and the average maximum field for 9 different thunderclouds was 1300 volts/ cm.
Abstract: Measurements of the electric field on the surface of aircraft flying through all types of weather and clouds are summarized. The measured electric field inside a thunderstorm just prior to a lightning strike at 12,900 feet was 3400 volts/cm. The average maximum field for 9 different thunderclouds was 1300 volts/cm. It is noted that large fields usually occur only inside the cloud and at altitudes somewhat comparable to the freezing level. Frequent reversals of the field are observed in these areas. The electric field measured inside a stable non‐precipitating cloud is less than 10 volts/cm.
TL;DR: In this paper, a semi-infinite body is assumed to be heated at a constant rate from the time t = 0 on, and the development of the temperature in this area and in its surroundings is calculated with certain simplifications.
Abstract: I. A circular area on a semi‐infinite body is assumed to be heated at a constant rate from the time t=0 on. The development of the temperature in this area and in its surroundings is calculated with certain simplifications.II. In a sliding contact the heat generated by friction is limited at every point to the time of contact. The temperature reached by the contact surface is calculated by aid of Part I and with assumptions about the size of the contact surface, which are based on earlier investigations of the author.Observations on the temperatures in bimetallic sliding contacts, indicating the contact temperature rise by means of a thermoelectric current, are compared with calculations partly according to the deduced theory partly according to an earlier published theory by Jaeger. A fairly good agreement is found with one exception.
TL;DR: In this article, a number of experiments directed toward determining the nature and cause of deposits which occur on electron microscope specimens under electron bombardment are described, and the conclusion is drawn that the material is a result of chemical reaction, occurring at any surface simultaneously bombarded by electrons and organic molecules.
Abstract: A number of experiments directed toward determining the nature and cause of deposits which occur on electron microscope specimens under electron bombardment are described. From these the conclusion is drawn that the material is a result of chemical reaction, occurring at any surface simultaneously bombarded by electrons and organic molecules. The organic vapors are shown to arise in two ways: (1) by diffusion out of the metal walls, gaskets, and greases exposed to the vacuum, (2) by the outgassing of metal parts of the instrument exposed to electron bombardment. To eliminate the effect both sources must be removed.
TL;DR: In this paper, a method for measuring absorption and velocity of ultrasonic radiation in the frequency range from 5 to 100 Mc by use of pulse techniques is described, and results of such measurements performed on polycrystalline magnesium and aluminum as a function of frequency and grain size show that the absorption coefficient varies linearly with frequency and inversely with grain size.
Abstract: A method for measuring absorption and velocity of ultrasonic radiation in the frequency range from 5 to 100 Mc by use of pulse techniques is described Results of such measurements performed on polycrystalline magnesium and aluminum as a function of frequency and grain size show that the absorption coefficient varies linearly with frequency and inversely with grain size The scattering power of a metal, and the fidelity with which an ultrasonic pulse is transmitted is shown to depend on the elastic constants of the single crystals Criteria are established for evaluating the fidelity of pulse transmission in cubic and hexagonal metals, and figures of merit for many such polycrystalline metals are given
TL;DR: In this article, a discussion of the properties of electromagnetic waves propagating with a velocity W < c. Boundary conditions are obtained for structures with very narrow slots, either closed or open, and a general method of solution of the wave equations is discussed.
Abstract: The paper is devoted to a discussion of the properties of electromagnetic waves propagating with a velocity W
TL;DR: In this article, a constantpotential electrostatic generator, together with an acceleration tube, was used to produce continuous streams of electrons with homo-geneous and controllable energy.
Abstract: In this work roentgen rays and cathode rays of several million‐volts energy have been applied to an investigation of their biological, photo‐chemical, and germicidal effects, particularly as they are related to the processing of foods and biological materials. A constant‐potential electrostatic generator, together with an acceleration tube, was used to produce continuous streams of electrons with homo‐geneous and controllable energy. [R. J. Van de Graaff, K. T. Compton, and L. C. Van Atta, Phys. Rev. 43, 149 (1943).] These high energy electrons were utilized both for the production of penetrating roentgen rays and for the direct irradiation of materials. The mechanism of the biological action of both roentgen rays and cathode rays is discussed, as well as the energy considerations in their application to various absorbers. The companion paper [C. G. Dunn, W. L. Campbell, H. Fram, and A. Hutchins, J. App. Phys. 19, 605 (1948)] reports on measurements of the lethal action of these radiations on a wide varie...