Volume 17, Issue 1, July 1945

Transmission, Reflection, and Guiding of an Exponential Pulse by a Steel Plate in Water. I. Theory
View Description Hide DescriptionIn this paper the problem of the interaction of an underwater explosionwave with a steel plate is discussed. Particular attention is given to those aspects of the problem in which the plate can be considered as an elastic, two‐dimensional wave guide. The phase velocities of the more important modes of the plate are evaluated as functions of frequency. They are used to derive the properties of the precursor, an oscillation which precedes the explosionwave as it travels along the plate. The results of the theory are compared briefly with experiment. A more detailed discussion of the experiments will be given in a second report. The methods used in this report are also applicable to the evaluation of the phase velocities of the modes of an electromagnetic‐wave guide. The propagation of a transient, such as an explosionwave, down a wave guide, presents the interesting mathematical problem of the evaluation of a contour integral of a function of a complex variable defined implicitly. No rigorous solution for this problem as yet exists.

Wave‐Front Determination in a Unidirectional Supersonic Beam
View Description Hide DescriptionAn experimental method has been developed to determine the loci of equal phase in a high frequency compressional wave beam in liquids without utilizing standing wave patterns. The wave front in a supersonic beam may thus be determined simultaneously with the relative excess pressure amplitude. The electric signal generated by the piezoelectric action of a Rochelle salt microphone which has the phase of the compressional wave in the liquid is combined with a small electric signal of the same frequency having the phase of the voltage impressed across the quartzgenerator. The result of this superposition is an approximately sinusoidal spatial variation of the signal generated by the microphone as the latter is moved in the direction of propagation of the beam. The wave front may be traced by following a maximum of this sinusoidal variation as the microphone is moved at right angles to the direction of propagation. The experimental data, taken around 1200 kilocycles, indicates the accuracy obtainable by the method.

Observed Classical Sound Absorption in Air
View Description Hide DescriptionA brief treatment of the theory and methods of measuringabsorption of sound in gases precedes the data which are presented in the form of curves. The measurements were made with a Pierce acoustic interferometer at a frequency of 1927 kc/sec. in air. This frequency is high enough to satisfy Hardy's and Krasnooshkin's required conditions to obtain reliable results by this method. The experimental result agrees with Krasnooshkin's value of .

A Working Standard for Sound Pressure Measurements
View Description Hide DescriptionThis paper discusses the necessary requirements to be met in an ideal sound pressuremeasurement standard. It also describes the design and shows the characteristics of a new microphone that meets these requirements to a greater degree than do existing units which are generally available for use as laboratory standards. The new microphone is stiffness‐controlled and has an acoustic impedance approximately equal to 0.001 cc of air throughout the entire audio‐frequency range up to 20 kc. The structure approximates rigid cylinder long and is linear to sound pressuremeasurements up to several million dynes/cm^{2}.

Application of the Wave Theory of Room Acoustics to the Measurement of Acoustic Impedance
View Description Hide DescriptionA method is presented for the measurement of acoustic impedance of large areas of material, at low frequencies, under actual mounting conditions and at various angles of incidence. It is then used to check the assumption in the wave theory of room acoustics that the boundary conditions for the sound field can be expressed in terms of a normal acoustic impedance which is not a function of angle of incidence. The impedance of material covering a wall is computed from two of the room's acousticproperties, the decay constants and frequencies of the normal modes of vibration. In this way the impedance of a large area that vibrates as a panel may be measured where determinations by methods using small samples are not applicable. By using large areas, the average impedance of a number of small samples may be obtained at once. The new method has the advantage that a direct and simple check of this value of the impedance may be secured by measurements of pressure distribution of the normal modes.

A Frequency Standard for Use at High and Low Frequencies
View Description Hide DescriptionA secondary frequency standard is described for use at high and low frequencies, consisting of a tuning‐fork oscillator which controls an Abraham and Block multivibrator. An amplifier of adequate selectivity allows the selection of any harmonic of the fundamental voltage. This is accomplished by the use of a multivibrator and a regenerative amplifier of high selectivity which allows selection of any harmonic of the fundamental frequency in the band 1 kc to 2 mc. The tuning‐fork oscillator presents the following advantages: 1. Possibility of adjusting the frequency by varying the amplitude of oscillation of the tuning fork. 2. Automatic adjustment of the amplitude to the desired value. 3. Automatic adjustment of the phase difference between the amplitude and the applied force. 4. Visual indication of amplitude. 5. Visual indication of the phase difference. 6. Possibility of manual adjustment of the phase difference. These properties permit indirect measurement of the frequency at any moment making it possible to change tubes without making necessary new calibration by comparison with a primary frequency standard.

Group Audiometry
View Description Hide DescriptionThe use of commonly available apparatus is described for a group test of auditory acuity as a function of frequency. Reliability is only slightly less than that of a careful individual examination. The techniques which produce highest reliability are described. Validity is satisfactory in terms of deviation from results of an individual test. The test is simple to take. Several checks on malingering are provided which make group audiometry practicable with populations not highly selected for age or intelligence.

Clinical Phenomena in Conductive Media: The Individual Earpiece
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Musicology, the Stepchild of the Sciences
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 LETTER TO THE EDITOR


Letter to the Editor
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 PROGRAM OF THE THIRTIETH MEETING OF THE ACOUSTICAL SOCIETY OF AMERICA


The Vibratron
View Description Hide DescriptionA continuously adjustable high Q electromechanical resonator, which may be used in the control of oscillators, pass‐band amplifiers, and the like. Applications of the device to laboratory apparatus, and to the telemetering and signaling fields, are described.

Transmission, Reflection, and Guiding of an Exponential Pulse by a Steel Plate in Water
View Description Hide DescriptionThe problem of the action of an underwater explosion—a pulse of the form p _{max} e ^{−t/τ}—on an elastic plate in water can be divided into two parts. In the first, the plate is considered as an infinite slab with the explosionwave as an incident plane wave transient. In the second, the plate is considered as a wave guide, with the explosionwave setting the initial conditions at the edge of the plate. The first is an inhomogeneous boundary value problem, the second a homogeneous one. The inhomogeneous case has been solved in the literature, for continuous waves, and the results of the theory are in qualitative agreement with the experiments on transients. The homogeneous problem forms the principal part of this paper. The phase velocity curves, as functions of frequency, for the principal normal modes of a plate in water, are closely related to the corresponding curves for a plate in a vacuum. The effect of the water on the principal symmetric mode of the plate is not to change the real part of the phase velocity from its value for a plate in a vacuum, but to add a small imaginary component, or attenuation due to radiation loss into the water. The principal antisymmetric mode is slightly attenuated at high frequencies, and strongly attenuated at low frequencies. The cut‐off comes at that frequency where the phase velocity along the plate equals the velocity of sound in water. In addition to these two modes, which correspond closely to the principal modes for a plate in a vacuum, the presence of the water introduces two additional modes, one symmetric and one antisymmetric. At high frequencies, their phase velocities are very close to, but a constant fraction of, the velocity of sound in water. At low frequencies, the phase velocity of the symmetric mode approaches the velocity of sound in water, the phase velocity of the antisymmetric mode approaches zero. Both these modes are unattenuated, i.e., their phase velocities are all real. The problem of the propagation of a transient in a wave guide presents the interesting mathematical problem, as yet unsolved rigorously, of the contour integral of a function of a complex variable defined implicitly. Brief comparison of the theory with experiment shows that the pure real antisymmetric mode accounts for most of the properties of the precursor. This is an oscillation which precedes the explosionwave along the plate, at a velocity slightly greater than that of sound in water, but less than that of rotational or dilational waves in the plate.

The Driving‐Point Impedance of an Infinite Solid Plate
View Description Hide DescriptionIn the design of mechanical filters whose function it is to prevent the transmission of vibration from one structure to another, it is necessary to know the impedances of the structures between which the filter is to be connected. In many of the cases which arise in practice, the impedance may be estimated from a knowledge of the driving‐point impedance of an infinite plate. An equation is presented for the impedance of an infinite plate of constant thickness when connection is made to the plate at a single point. The impedance may be written in the form 8ρh ^{2} v, where ρ is the density, h the thickness of the plate, and v a velocity approximately equal to the velocity of shear waves in the material. It is shown that the driving point impedance is equal, except for a constant factor, to the impedance of a mass equal to the mass of a disk cut from the plate whose radius is the mean proportional of the thickness and the wave‐length which corresponds to v. The results are exemplified by applying them to the case of a steel plate.

Absorption and Scattering by Absorbent Cylinders
View Description Hide DescriptionThe absorption and scattering of a plane wave by an infinitely, long circular cylinder, whose axis is perpendicular to the direction of propagation of the wave, are calculated. The surface of the cylinder is assumed to have a known normal acoustic impedance.Absorption measurements made on long cylinders placed in a reverberation room (where the incident wave directions are at all angles to the axes of the cylinders) are comparedz with the computed values.

Theory of the Effect of Wall Irregularities on the Distribution of Sound in a Room
View Description Hide DescriptionThe perturbation theory of Feshback and Clogston can be applied to determine the amount of wall irregularity required to produce adequate “randomness” in the sound waves in a room. When the second‐order terms in the perturbation series are as large as the first‐order terms, then each standing wave is a complete mixture of all the types of simple waves, and the decay rate approaches that predicted by the Sabine formula. From this criterion one can obtain an “index of randomness,” which is a measure of the ability of the room to “mix” sound of a given frequency adequately. If the index is much smaller than unity, the sound will not be well mixed, and the decay curve will be a curved line (Sabine formula will not hold). If the index is much larger than unity, the Sabine formula will hold. Approximate formulas for the index show that irregularies in wall shape are usually more effective (in mixing the sound) than irregular patches of absorbing material, that patches (or bumps) of the order of size of a half‐wave‐length are more effective than larger or smaller ones, and that rooms large compared to the wave‐length are easier to “randomize” than smaller rooms. It is quite difficult to treat a room of dimensions smaller than ten wave‐lengths so that the index of randomness comes out larger than unity.

Influence of Room Proportions on Normal Frequency Spacing
View Description Hide DescriptionProportioning of rectangular rooms to give smooth low frequency response has been guided by an empirical rule: dimensions should be related by ratios of or its powers. An analytical basis for a criterion is being explored. Normal frequencies and their distributions are expressed in generalized terms, using dimensions L, pL, qL, and a dimensionless frequency parameter μ. Distributions of μ can be investigated as a function of proportions (p, q) alone, holding volume constant. A frequency spacing index Ψ is obtained by averaging the ratio of actual to average spaces, weighted by the width of each space. The index Ψ increases with increasing fluctuation from uniform spacing; Ψ = 1 for uniform spacing; Ψ = 2 for random (Poisson) distribution. The index has been evaluated numerically over arbitrary frequency intervals, for a number of room proportions. As expected, Ψ is large (>2) for a cube and other proportions with simple ratios. The index has a small value (<1.5) over ranges of incommensurate p, q values. The “ rule” gives results in the low region, but is apparently not a unique measure of optimum smoothness. These calculations are approximately correct for basically rectangular rooms having irregularities (e.g., polycylindrical diffusers) appreciably smaller than wave‐lengths involved. Room proportions, and the Ψ‐criterion, are probably not important when room dimensions are longer than about 10 wave‐lengths, as adequate diffusion can then be obtained by shape irregularities and absorption.

Detection of Resonances in Vibratile Members by Measurement of Electro‐Magnetically Induced Voltages
View Description Hide DescriptionAn instrument is described by which the velocity versus frequency characteristics of a conducting filament or similar vibratile member may be detected, regardless of the inaccessibility of the member. The assembly to be studied is submerged in a known magnetic field and subjected to vibration over the audio range. The voltage generated in the vibratile member is amplified and this indicates the integrated vibration velocity of the member.

Headphone Measurements and Their Interpretation
View Description Hide DescriptionMethods of acoustical measurement and of data presentation are reviewed, with emphasis on relating headphone data to the requirements of the communication and monitoring fields of application. The conditions of headphone listening are compared to standard and typical listening conditions, as an aid to the interpretation of headphonemeasurements. Data are shown to demonstrate the importance of statistical analyses of the performance of headphones on different wearers. Some effects of presenting too “artificial” an acoustical load to the receiver during measurement are illustrated. An experiment in artificial ear development is described. The requirements for an improved artificial ear are outlined, based in part upon the experimental work.

Basic Measurements on the Physical Characteristics of Speech Transmission Systems
View Description Hide DescriptionThis paper discusses proposed American standardization of basic tests on the physical characteristics of speech transmission systems.
