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Journal of the Acoustical Society of America

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Nov 1953

Volume 25, Issue 6, pp. 1037-1203

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On the Theory and Design of Acoustic Resonators

Uno Ingard

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1037-1061 (1953); (25 pages) | Cited 35 times

Online Publication Date: 29 Jun 2005

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Absorption and scattering from resonators in a free field as well as in walls are discussed. The effect of different aperture geometries on the resonance frequency of resonators is considered and illustrated by examples. Considering losses due to viscosity, heat conduction, and radiation, the optimum design for maximum resonance absorption is analyzed, and the results are expressed in terms of design charts. Nonlinear effects on the absorption and resonance frequency are also included, and a discussion of the onset of turbulence is presented.

The Near Field of a Helmholtz Resonator Exposed to a Plane Wave

Uno Ingard

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1062-1067 (1953); (6 pages)

Online Publication Date: 29 Jun 2005

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The near field of a spherical Helmholtz resonator exposed to a plane wave is computed and shown to be in good agreement with measurements. Comparison is made with the near field of a resonator terminating a cylindrical tube. A discussion of the calculation of the dissipation in the resonators is included.

A Study of the Factors Influencing the Damping of an Acoustical Cavity Resonator

Robert F. Lambert

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1068-1083 (1953); (16 pages) | Cited 2 times

Online Publication Date: 29 Jun 2005

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This paper presents a systematic study of experimentally significant losses contributing to the damping of an acoustical cavity resonator. Absorption measurements in air on the 0, 1 wave of a round cavity were made by a resonance response method employing a transverse particle velocity pickup device. This study reveals that mechanical losses due to the vibrations of the walls are experimentally significant. Empirical relaxation time formulas are established for air at 24 and 27°C. The thermal and viscous boundary‐layer loss formula is fitted to these data by choosing the thermodynamic ratio νρ0/μ equal to 1.31.

The Attenuation of Sound in Small Tubes

G. T. Kemp and A. W. Nolle

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1083-1086 (1953); (4 pages)

Online Publication Date: 29 Jun 2005

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An experimental investigation of the attenuation of sound in two air‐filled tubes of 0.238 and 0.0292 cm inside radius in the frequency range from 3.8 to 20 kc was conducted, and the results were compared with values of attenuation calculated from the Kirchhoff theory for rigid walled tubes. Agreement of experimental with theoretical values was found within the accuracy of the experiment, provided that the comparison made only with the portion of attenuation proportional to square root of frequency, as suggested by Fay. The attenuation was determined by a method which was different, in some respects, from those previously employed. The variable length, closed tube was driven with a high‐impedance source, and the input pressure was sampled with a high‐impedance microphone probe. The input pressure was recorded as a function of closed tube length. Since the input pressure can be assumed to be proportional to input impedance for these conditions, the attenuation can readily be determined from the ratio of the pressure maxima or minima.

On Radiation and Scattering from Small Cylinders

John W. Miles

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1087-1089 (1953); (3 pages)

Online Publication Date: 29 Jun 2005

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The original work of Rayleigh on scattering and radiation of harmonic disturbances by small cylinders is extended to transient disturbances. The analysis is closely related to Ward's treatment of the aerodynamics of slender bodies in supersonic flow.

Scattering of Underwater Plane Ultrasonic Waves by Liquid Cylindrical Obstacles

Stanley J. Bezuszka

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1090-1095 (1953); (6 pages)

Online Publication Date: 29 Jun 2005

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This paper is a report of a theoretical investigation of sound scattering from liquid cylindrical obstacles immersed in water following closely the conditions prevailing in the previous experimental work of Tamarkin, Bauer, and others. An incident plane wave being assumed, series solution was found for the total scattered wave. Numerical calculations were carried out using parameters approximating those of Tamarkin's experiments (radius of obstacle, 0.635 cm; sound frequency, 1.145 mc/sec; wavelength, 0.13 cm). A series of scattering patterns, confined principally to the forward direction for an angular spread of about 14° (with the obstacle at the vertex) were calculated for eight liquids, chosen to give a spread of kia values (ki the wave parameter inside the liquid and a the radius) between 26.0 and 41.0. The results of this theoretical investigation confirm the experimental findings that for the liquids examined the scattering is diffractive and lies in the zone between the geometrical region and the region of Rayleigh scattering. Quantitative comparisons are made between the theoretical and experimentally plotted results with special emphasis on the experimental resonance curve and its theoretically computed counterpart.

The Scattering of Sound in a Turbulent Medium

Robert H. Kraichnan

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1096-1104 (1953); (9 pages) | Cited 17 times

Online Publication Date: 29 Jun 2005

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The scattering of a sound wave in a medium undergoing shear flow confined to a finite region is investigated under the assumption that the total velocity field is everywhere small compared to the velocity of sound. Formulas are obtained for the angular distribution and frequency distribution of the scattered wave in terms of the four‐dimensional Fourier transform of the shear velocity field.
Under typical conditions, the cross sections for the scattering of a plane wave of frequency ω by a shear flow of given scale and spatial structure are approximately of the form ω4M2, where M is a characteristic Mach number of the flow. The coupling between the shear and longitudinal velocity fields has a tensor character such the the scattering vanishes at 180 degrees and at 90 degrees. The spectrum of the scattered sound wave is very sharp in the forward direction and becomes broader at larger scattering angles.
Explicit expressions for the cross sections are obtained for the case of scattering from a region of isotropic turbulence. When the frequencies of importance in the turbulence are small compared to the frequency of the incident sound wave, the average differential scattering cross section can be expressed directly in terms of the energy spectrum of the turbulence.

Reflection of Acoustic Waves from an Inhomogeneous Fluid Medium. I

G. S. Heller

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1104-1106 (1953); (3 pages)

Online Publication Date: 29 Jun 2005

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The reflection coefficient for plane waves incident obliquely on a medium in which the velocity decreases exponentially is computed approximately using the WKB method and compared with a computation from the rigorous solution. The approximate reflection coefficient 1/[16(ω/g)2 cos6θ+1] where ω is the angular frequency, g is the velocity gradient at the start of the exponential decrease, and θ the angle of incidence is within 0.05 percent of the rigorous value for ω/g ⩾ 5 at normal incidence and within 5 percent of the rigorous value for ω/g ⩾ 20 for angles of incidence up to about 45°.

Wave Propagation in a Randomly Inhomogeneous Medium. II

David Mintzer

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1107-1111 (1953); (5 pages) | Cited 6 times

Online Publication Date: 29 Jun 2005

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The region of validity of the single‐scattering approximation used in Part I is found by considering the next higher approximation; it is valid for k02arα2≪1, where k0 is the wave number of the incident sound, r is the range from source to observer, a is the mean size of the inhomogeneities, and α is the rms value of the refractive index variations. Some approximate results are given for the case of wavelength large compared with inhomogeneity size. By consideration of the intensity variations, it is found that ray theory is valid for (k0a2/r)≫1, as has been found for plane waves.

Apparatus and Procedure for Measuring the Absorption of Sound in Gases by the Tube Method

F. A. Angona

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1111-1115 (1953); (5 pages) | Cited 3 times

Online Publication Date: 29 Jun 2005

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An apparatus for measuring the absorption of sound in gas mixtures has been developed and tested. The apparatus consists of a sound tube, a movable ribbon‐type speaker, and a fixed condensor microphone. The absorption is determined by recording the sound pressure as the path length between the speaker and the microphone is increased. The measured attenuation coefficient is corrected for the effect of the tube and also for the attenuation due to the viscosity and heat conduction of the gas. Both frequency and pressure are variable and range from 2 to 10 kc and from 3 to 300 mm of Hg, respectively.

The Absorption of Sound in Gas Mixtures

F. A. Angona

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1116-1122 (1953); (7 pages) | Cited 6 times

Online Publication Date: 29 Jun 2005

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The absorption of sound has been measured in CO2, CS2, C2H4O, and in mixtures of the latter two gases with CO2 for frequencies ranging from 2 to 10 kc and for pressures ranging from 3 to 300 mm of Hg. The tube method was employed. The absorption was determined by observing the decrease in sound pressure as the path length between the speaker and the microphone was increased. A fixed condensor microphone and a movable ribbon‐type speaker were used.
The measured absorption coefficient was corrected for the effect of the tube and also for the absorption due to viscosity and heat conduction of the gas. The corrected absorption coefficient was then plotted as the attenuation coefficient per wavelength against the logarithm of the ratio of frequency over pressure. These curves were then compared to those determined from Bourgin's Theory for mixtures of absorbing gases. The agreement between the observed attenuation and that predicted by the theory was within 5 percent.

Acoustic Streaming near a Small Obstacle

Peter J. Westervelt

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1123-1123 (1953); (1 page)

Online Publication Date: 29 Jun 2005

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Steady rotational flow is known to occur in the vicinity of a smooth rigid object oscillating to and fro in a viscous incompressible fluid. For a small oscillation amplitude the steady flow is shown theoretically to be invariant to the coordinate transformation which renders the object stationary.

The Measurement of the Velocity of Sound in Liquids

G. M. Graham

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1124-1127 (1953); (4 pages)

Online Publication Date: 29 Jun 2005

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A new technique for the measurement of sound velocity in liquids has been developed, which is especially suited to frequencies in the range from 0.5 to 5 mc. It employs an approximation to the boundary conditions in Guptill's closed form solution for the radiation field between two infinite walls with a piston source in one wall.
Measurements have been made in distilled water at 0.6 and 7.6 mc with an error of less than 0.2 percent in the low‐frequency measurements. No dispersion is indicated to the order of the experimental error, in the temperature range from 10 to 20°C.
A description of the apparatus is given.

A Simple Calibration Technique for Low‐Sensitivity Transducers

William J. Galloway

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1127-1129 (1953); (3 pages)

Online Publication Date: 29 Jun 2005

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The cavitation threshold of water supersaturated with air at hydrostatic pressure is utilized as a pressure reference level against which the output of a transducer may be referred. The threshold may be determined within 0.2 decibel in a purely radial standing‐wave field. A simple system is described for performing the measurements.

Electronic Sound Absorber

Harry F. Olson and Everett G. May

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1130-1136 (1953); (7 pages) | Cited 24 times

Online Publication Date: 29 Jun 2005

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The electronic sound absorber is so named because it absorbs sound or reduces the sound level by means of an electronic transducing system, as contrasted to conventional sound absorption by direct conversion from acoustical to heat energy. The electronic sound absorber consists of a microphone, amplifier, and loudspeaker connected so that, for an incident sound, wave and sound pressure at the microphone is reduced. Thus it will be seen that the electronic sound absorber is a feedback system which operates to reduce the sound pressure in the vicinity of the microphone. The sound pressure in the neighborhood of the microphone can be reduced 10 to 25 decibels over a frequency range of three octaves in the low‐frequency portion of the audio‐range. The electronic sound absorber may be used to reduce the noise over a small volume, that is, spot type noise reducer or it may be used with an acoustical resistance to obtain a high order of sound absorption in the low‐frequency range.

Measurements on Nonreciprocity in an Electromechanical System

L. J. Black and H. J. Scott

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1137-1140 (1953); (4 pages)

Online Publication Date: 29 Jun 2005

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Relations for an electromechanical network that contains both electrostatic and electromagnetic coupling and has the antireciprocal transfer characteristic described by McMillan are developed. The effect of hysteresis and eddy currents is included. An equivalent electrical circuit that makes use of the “ideal gyrator” to give the antireciprocal characteristics presented. Several sets of experimental measurements are described which clearly show the nonreciprocal characteristics of the system.

Distortion in Phonograph Reproduction

H. E. Roys

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1140-1144 (1953); (5 pages)

Online Publication Date: 29 Jun 2005

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Three distortion methods, the harmonic, the SMPE intermodulation, and the CCIF (a difference frequency), have been studied, mainly on a theoretical basis, as a means of analyzing distortion encountered in phonograph reproduction. The harmonic method is somewhat difficult to apply and some of the harmonics may be beyond the range of the system. The IM has been used in the past with considerable success, and appears to be a good method of analyzing tracing distortion. The difference frequency methods appears to be somewhat insensitive to tracing distortion but offers theoretical advantages in that the analysis may be made right up to the cut‐off frequency of the system, practically it is somewhat difficult to apply.

Electro‐Optic Sound‐on‐Film Modulator

Robert O'B. Carpenter

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1145-1148 (1953); (4 pages) | Cited 2 times

Online Publication Date: 29 Jun 2005

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The electro‐optic effect in the crystal ammonium dihydrogen phosphate provides a high‐speed light valve with ruggedness, long life, and ease of handling not possessed by the similar Kerr effect in liquids. In this paper the design of a practical sound reproduction unit for making variable density 35‐mm tracks will be described. Frequency response of the light valve is flat to over 20 000 cycles, the over‐all system being limited to about 10 000 by the slit‐width film speed effect. Tests of distortion and sound quality in the sound tracks obtained are described.

On the Mechanism of the Photographic Effect of Ultrasonic Waves

G. S. Bennett

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1149-1151 (1953); (3 pages)

Online Publication Date: 29 Jun 2005

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Experimental data are submitted indicating the existence of a direct action of ultrasonic waves on a photographic emulsion, contrary to the views of some other workers. All of the evidence obtained here indicates a closer correlation with the softness of the emulsion than with the known behavior of ultrasonically produced luminescence. Information is presented as to temperature dependence of the image, effect of ambient pressure, light shielding, and the behavior of various types of commercial emulsions.

An Acoustic Lens as a Directional Microphone

Malcolm A. Clark

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1152-1153 (1953); (2 pages)

Online Publication Date: 29 Jun 2005

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An acoustic lens combined with a conical horn can be used to obtain a highly directional microphone without some of the disadvantages of the parabolic microphone. The directional characteristics can be calculated satisfactorily if one assumes that the horn provides uniform flooding of the lens aperture.

A Tone Burst Generator

Kerim Onder

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1154-1156 (1953); (3 pages)

Online Publication Date: 29 Jun 2005

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A tone burst generator is described for the production of electronically keyed oscillations free of transients. The unit consists of an oscillator, a keying circuit, and a negative pulse generator with variable duration and repetition rate. The advantages of the tone burst method in testing the frequency and transient response of amplifiers and transducers are pointed out. Some applications including reverberation time measurements are also mentioned. The almost instant rise and decay of the tone bursts was achieved by providing practically zero impedance path to ground for the keying pulses.

The Measurement of Noise with the Sound Spectrograph

Gordon E. Peterson and Gordon Raisbeck

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1157-1162 (1953); (6 pages)

Online Publication Date: 29 Jun 2005

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The sound spectrograph principle may be employed in the quantitative measurement of noise. Measurements may be made with the conventional amplitude section circuit in which, in the customary use of the sound spectrograph, each section provides observation during a few milliseconds of the signal time. A long integrating time circuit for the amplitude sectioner has been developed which provides integration over a period of as much as one or two seconds of signal time. The amplitude sectioning circuit of the sound spectrograph may be employed to determine the relationship between the level of a pure tone and the power‐per‐cycle of noise. Measurements were made for various types of amplitude analysis with the sound spectrograph. A study was made of the degree to which the section displays conform to the computed values of noise level.

A Practical Noise Reduction Treatment for Diesel Engines

James E. Ancell

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1163-1166 (1953); (4 pages)

Online Publication Date: 29 Jun 2005

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A noise reduction treatment for Diesel engines is described, which, though not the ideal approach to the problem, is practical, economical, and applicable to both new engines and those already in service in the field. This treatment was designed making use of the results of a survey of the relative importance of the various noise sources on the Diesel engine. The treatment consisted of a set of sheet metal covers, lined internally with acoustical absorbing material, which were mounted directly over the noisy areas of the engine by means of built‐in vibration isolation. Noise reductions for the direct sound were at least 8 to 12 db, which were observed at a distance of one foot from the engine. The total loudness of the engine noise at six feet was reduced from 320 to 220 sones. This is a substantial improvement with regard to voice communication in the immediate vicinity of the engine. The speech interference level of the engine noise at six feet was reduced from 87 to 82 db.

A New Integral Ratio Chromatic Scale

Theodore E. Simonton

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1167-1175 (1953); (9 pages)

Online Publication Date: 29 Jun 2005

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The IRC scale presented herein is neither a Pythagorean scale, nor a just scale, nor an equally tempered scale, as those terms are defined in Acoustical Terminology, but it is shown to possess the major advantages of all three. In a D‐D octave, all of the notes are interconnected by a perfectly symmetrical arrangement of just fourths, and the note frequencies of the octave containing C4=256 cps are 144, 153, 162, 171, 180, 192, 204, 216, 228, 240, 256, 272, 288. A distinguishing characteristic of the IRC scale is that four ascending octaves commencing with a C embrace exactly four successive just fifths (C‐G‐D‐A‐E) immediately followed by four successive just fourths (E‐A‐D‐G‐C). The IRC scale, like the conventional just scale, is based on alternately conjunct and disjunct just tetrachords, but the IRC tetrachord intervals are the smoothly decreasing ones of 9:8, 10:9, 16:15, instead of the just scale irregularly arranged intervals of 16:15, 9:8, 10:9. The major and minor tones of the IRC scale are divided by the known superparticular proportion, giving, in addition to the just semitone 16:15, semitone ratios of 17:16, 18:17, 19:18, and 20:19. These five semitones are located in smoothly progressing order, forming three perfect harmonic series embracing a just major third, fourth, and minor third. The IRC scale is shown to be superior to the just and Pythagorean scales and to excel the equally tempered scale in modulation. If, as the author believes, Helmholtz was correct in his thesis that just intervals are musically better than equal tempered intervals, then the IRC scale is also superior to the equally tempered scale, possessing, among many other advantages, greater ease of tuning pianos and organs, and the ability to tune pianos, violins, and cellos exactly alike and play them in the same temperament.

Masking of Speech by Bands of Noise

I. J. Hirsh and W. D. Bowman

J. Acoust. Soc. Am. Volume 25, Issue 6, pp. 1175-1180 (1953); (6 pages) | Cited 1 time

Online Publication Date: 29 Jun 2005

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The threshold of intelligibility for two‐syllable (spondee) words was measured in the presence of different levels of masking noise. Twelve different bands were used, one (20 to 6600 cps) approximating a white noise and each of the other eleven containing a band of frequencies corresponding to a pitch interval of 250 mels. The absolute thresholds for these bands were also measured to permit transformation of the noise level from an absolute scale to a scale of sensation level.
The results show linear relations between the masked threshold and noise level for white noise and for bands of noise between 394 and 1420 cps. For noise bands above 1420 cps this masking function is accelerated, while the two bands below 394 cps yield sigmoid masking functions. Of the bands used, the most effective contained frequencies between 670 and 1000 cps. The signal‐to‐noise ratio at threshold for this band was about −25 db while for bands above or below it became gradually smaller than −25 db, reaching a minimum of −60 db for the highest and lowest bands. White noise was more effective than any band, giving a threshold S/N ratio of −15 db.
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