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Journal of the Acoustical Society of America

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Nov 1955

Volume 27, Issue 6, pp. 1019-1227

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Notes on the Exact Equations Governing the Propagation of Sound in Fluids

Frederick V. Hunt

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1019-1039 (1955); (21 pages) | Cited 7 times

Online Publication Date: 29 Jun 2005

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The assumptions underlying the exact equations of motion for a thermoviscous fluid are reviewed and the complete equations are given, for reference convenience, in both tensor and vector form. The first‐ and second‐order acoustic equations are then exhibited and used to obtain the source terms that account for the generation of vorticity and streaming. In order to preserve a broad base from which to make the approximations appropriate under various circumstances, all terms are retained explicitly including those arising from any functional dependence of the viscosity and thermal coefficients on the state variables.
The distinction between spatial and material coordinate systems is carefully drawn and conversion transforms are derived rigorously and their use illustrated. The general properties of finite‐amplitude waves are demonstrated by including the second‐order terms in a plane‐wave solution of the exact wave equation in material coordinates, with special concern for the effects of large amplitude on speed of propagation and on wave‐form distortion.
Sound absorption and dispersion measures for a viscous conducting fluid are analyzed in terms of Truesdell's recent exact solution of the first‐order secular equation. These differ characteristically from the corresponding measures predicted for pure relaxation in a two‐fluid mixture. It is concluded that a complete and adequate theory of sound absorption and dispersion will need to take into account both relaxation and viscothermal phenomena as well as their interaction, and that until such a general theory is available, the exact theory of viscothermal effects—rather than the crude linear approximation commonly, but inappropriately, called “classical”—should be used in computing the “excess” absorption and dispersion to be accounted for by relaxation processes.
The exact solutions of the secular equation permit a new evaluation, in series form, of the characteristic acoustic impedance for a thermoviscous medium. The notes conclude with a revised account of the spectral character of thermal noise in the acoustic medium based on the quantum hypothesis and a merger of the concepts of architectural acoustics and specific‐heat theory.

Heat Conduction Losses in the Acoustic Boundary Layer

James E. Young

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1039-1043 (1955); (5 pages)

Online Publication Date: 29 Jun 2005

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The attenuation resulting from heat conduction of the quasi‐plane mode in a cylindrical conduit is discussed in the high‐frequency (narrow boundary layer) limit. The heat conduction part of the Kirchhoff losses is derived by means of a volume integral whose physical interpretation can be given.
Preliminary to considering the Kirchhoff case, the heat conduction attenuation of a plane wave is computed to illustrate the use of the integral form.
Finite thermal conductivity of the walls, as it gives rise to attenuation in guided propagation, is also discussed.

Reflection and Transmission of Sound by a Moving Medium

Joseph B. Keller

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1044-1047 (1955); (4 pages) | Cited 4 times

Online Publication Date: 29 Jun 2005

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The reflection and transmission of sound by a moving medium are investigated theoretically and the reflection and transmission coefficients are determined. These coefficients are found to depend only upon that component of the velocity of the medium which lies in the plane of incidence. The reflection coefficient increases with the velocity of the moving medium until a velocity is reached at which total reflection occurs. Total reflection persists until a still higher velocity is reached above which the reflection coefficient decreases as the velocity increases.

Structure and Velocity of the Periodic Vortex‐Ring Flow Pattern of a Primary Pfeifenton (Pipe Tone) Jet

A. B. C. Anderson

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1048-1053 (1955); (6 pages) | Cited 2 times

Online Publication Date: 29 Jun 2005

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Visualization of the vortex flow pattern in typical primary Pfeifenton jets was made by means of shadow‐graph techniques to show the transition in form of the vortex pattern as it moves downstream in the jet, as well as, the dependence of the downstream translational vortex velocity and the geometry of the vortex pattern on the Reynolds number of the jet.
Results of experiment are compared with available theory. These studies were carried out with carbon dioxide jets discharging into the atmosphere. The flow channel geometry consisted of a pipe ⅞ in. in diameter, 12.013 in. long effectively, open at one end which was inserted into a large stilling tank and terminated at the other end by an orifice plate containing a sharp‐edged circular orifice, 0.250 in. in diameter and 0.093 in. thick.

Entropic Equations of State and Their Application to Shock Wave Phenomena in Solids

George E. Duvall and Bruno J. Zwolinski

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1054-1058 (1955); (5 pages) | Cited 8 times

Online Publication Date: 29 Jun 2005

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The front of a shock wave in an ideal fluid is characterized by a discontinuous transition from the undisturbed state to a highly compressed state in which the entropy of the fluid has increased. The relations between pressure, density, propagation velocity, and particle velocity behind the shock front are represented by the equations for conservation of mass, momentum, and energy and by the equation of state of the fluid. The entropy change produced by the transition is third order in the compression for weak shocks. The propagation of shock waves through metals can be described by a hydrodynamic theory which assumes that the metal is an ideal fluid behind the shock front, and that the hydrostatic equation of state is applicable there. Three hydrostatic equations of state for Al, Cu, Fe, and Pb are compared with experimental data at low pressures and quantum mechanical calculations pressures up to several hundred megabars. With these equations of state the hydrodynamic theory is used to calculate explicitly the entropy increase across the shock front, the amount by which the pressure exceeds the adiabatic pressure for a given compression, and the temperature rise after the shock pressure has been relieved for the metals mentioned above.

Vibration of Simply Supported Isosceles Trapezoidal Flat Plates

Bertram Klein

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1059-1060 (1955); (2 pages)

Online Publication Date: 29 Jun 2005

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Solutions are given for the lowest natural frequency of flexural vibration of isosceles trapezoidal flat plates which have simply supported edges. The results of the calculations are presented graphically so that one may determine rapidly a desired fundamental frequency. The range of the values of the geometric parameters defining the plate is large enough to cover most practical cases.

Propagation of Sound in Thin Elastic Shells

James E. Young

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1061-1064 (1955); (4 pages)

Online Publication Date: 29 Jun 2005

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A wave theoretical analysis of symmetric mode propagation in a medium confined by a cylindrical elastic shell is carried out. An expression is obtained for the axial propagation constant, specialized to that case of a thin steel shell surrounding a column of air. This is further restricted to the description of the lowest symmetric mode.
The dispersion predicted by the analysis is in order of magnitude agreement with that obtained on a transmission line picture.

Phase Velocities and Displacement Characteristics of Free Waves in a Thin Cylindrical Shell

P. W. Smith, Jr.

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1065-1072 (1955); (8 pages) | Cited 7 times

Online Publication Date: 29 Jun 2005

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Results are presented giving values of the phase velocities and the relative magnitudes of the components of displacement for all possible free waves in the wall of a thin, elastic, cylindrical shell. Three classes of waves are identified and their natures are discussed as frequency is varied continuously. The vibrations are interpreted not only as standing waves and waves progressing the axial direction, but also as fully free waves traveling in a helical direction in the wall of the cylinder.

Measurement of Correlation Coefficients in Reverberant Sound Fields

Richard K. Cook, R. V. Waterhouse, R. D. Berendt, Seymour Edelman, and M. C. Thompson, Jr.

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1072-1077 (1955); (6 pages) | Cited 20 times

Online Publication Date: 29 Jun 2005

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Reverberation chambers used for acoustical measurements should have completely random sound fields. We denote by R the cross‐correlation coefficient for the sound pressures at two points a distance r apart. R  =  〈p1p2〉Av/(〈p12〉Av〈p22〉Av)½, where p1 is the sound pressure at one point, p2 that at the other, and the angular brackets denote long time averages. In a random sound field, R = (sinkr)/kr, where k = 2π/(the wavelength of the sound). An instrument for measuring and recording R as a function of time is described. A feature of this instrument is the use of a recorder′s servomechanism to measure the ratio of two dc voltages. The results of correlation measurements in reverberant sound fields are given.

Acoustical Properties of Carpet

Cyril M. Harris

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1077-1082 (1955); (6 pages)

Online Publication Date: 29 Jun 2005

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The acoustical properties of carpet are of interest in the design of auditoriums and studios, since the absorption which it contributes may be quite significant. However, little data exist on the acoustical properties of carpet and the scanty data available make no distinction among the various types of carpet. This paper describes measurements of the normal absorption coefficient and flow resistance for a wide variety of carpet samples. The normal absorption data were used to investigate which of many variables in carpet construction are important from the standpoint of acoustical absorption. On the basis of these data, certain key samples were selected for chamber test at the National Bureau of Standards for comparison with the tube measurements.

Acoustical Streaming in the Vicinity of a Sphere

C. A. Lane

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1082-1086 (1955); (5 pages) | Cited 5 times

Online Publication Date: 29 Jun 2005

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Recent studies have led to a satisfactory understanding of the details of acoustical streaming in the vicinity of a cylinder. Similar studies have now been completed for a sphere. In general, the steady flow around a sphere and the characteristic parameters are very much like what has been found for the cylinder. An experimental verification of the theory has been attempted by comparing the observed dc boundary‐layer thickness with that found from the theory. This is summarized in a curve of δdc/δac vs a/δac, where δdc is the dc boundary‐layer thickness, δac is the ac boundary‐layer thickness, and a is the radius of the sphere.

Study of Acoustical, Requirements for Teaching Studios and Practice Rooms in Music School Buildings

R. N. Lane and E. E. Mikeska

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1087-1091 (1955); (5 pages)

Online Publication Date: 29 Jun 2005

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Acoustical measurements are presented on teaching studios and practice rooms of several music buildings located at four southwestern universities. Data were taken on a wide range of wall construction and recommendations on room response and acoustical isolation between rooms are presented.

Fluctuations in Intensity of Short Pulses of 14.5‐kc Sound Received from a Source in the Sea

F. H. Sagar

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1092-1106 (1955); (15 pages) | Cited 1 time

Online Publication Date: 29 Jun 2005

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Some 4000 measurements of acoustic pressure obtained from experiments (using 1.3‐millisecond pulses), in which resolution was achieved between direct and echo pulses, are reported. Of the usual causes producing fluctuation, many were either eliminated or corrected for. Transducer oscillations of the linear and rotational types remained, together with attenuation changes due to temperature‐microstructure effects. Two ships were employed, both multianchored to ensure range constancy, work being restricted to conditions of low sea state and to ranges of from 70 to 500 yards. The depths of the projector and the hydrophones were respectively 60 and 45 ft. The area selected was about 50 miles from the mainland of the North Island of New Zealand and here only small streams drain from the coast into the sea. Work was performed in a 130‐foot patch of secluded water between a few steep rocks and islands, the drainage from the latter also being negligible. Fluctuation from signal to signal was small, the largest value of the ratio “maximum pressure to minimum pressure” for the longest experiment (85 minutes) being 1.94 while the variation coefficients for 48 separate pulse sequences relating to a variety of conditions fell in the range 5.0% to 12.4%. No clear correlation was found to exist between fluctuation and range, transducer depth or tidal current, but some correlation existed with sea state. Percentage deviations from the average pressure‐signal value per hydrophone, gave histograms, for any one experiment, which are approximately Gaussian in shape, the largest value of deviation encountered being plus 40%. Histograms constructed from data from selected hydrophones possessing identical spatial irregularities have a modified shape consistent with the conclusion that fluctuation is here entirely due to continuous transducer rotations about the suspension cables.

Fixed Path, Variable Frequency Acoustic Interferometer

Herman I. Leon

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1107-1112 (1955); (6 pages) | Cited 1 time

Online Publication Date: 29 Jun 2005

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A fixed path, variable frequency acoustic interferometer is described that is particularly suited for measuring ultrasonic velocities in liquids as a continuous function of temperature and pressure of the medium. The interferometer contains two clamped crystals: one, a low intensity ultrasonic source; and the other, a fixed, parallel reflector. The frequency of excitation, supplied from a frequency generator, is varied, and cyclic changes in input impedance are detected in an impedance bridge circuit. Crystal resonance is avoided. The interferometer, addition to the usual advantages of a fixed path system over a variable path one, operates at very low power levels; hence, it avoids problems occasioned by high intensity pressure waves. Frequency, the measured variable, is one that can be precisely measured with comparative ease.
The complete equivalent network for either the fixed or variable path interferometer is presented, from which the operation of the fixed path, variable frequency system is derived. The effect of crystal backing impedance is discussed, and the characteristics of the interferometer are shown to be those of a double crystal interferometer having infinite backing impedance.
The velocity of sound in water is measured between 25 and 53°C in the frequency range of 600 to 800 kc. At 25.0°C the measured velocity is 1496.8±0.3 meters/second, and the temperature coefficient is +2.7 meters/second °C.

Fundamental Acoustics of Electronic Organ Tone Radiation

Daniel W. Martin

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1113-1119 (1955); (7 pages)

Online Publication Date: 29 Jun 2005

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The acoustical effects achieved and the techniques used in the radiation of organ tone are quite different from the conventional effects and practices of public‐address sound systems. For the latter, point‐source radiation with high uniform directivity and a minimum of reverberation are sought, in general, for the creation of the illusion of “presence” of the original sound source. However in organ music the sound sources and their images are widely distributed in space. This is especially true in those typical cases where the tone sources are enclosed in an organ chamber, or are installed in a highly reverberant environment. Another distinctive feature of organ tone radiation systems is the relative importance of the octave below 60 cps. This paper contains design principles for electronic organ tone chambers and describes several types of organ tone cabinets now in use. Examples of the application of organ installation principles are given.

Directional Properties of Continuous Plane Radiators with Bizonal Amplitude Shading

Gordon E. Martin and John S. Hickman

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1120-1127 (1955); (8 pages)

Online Publication Date: 29 Jun 2005

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The problem of reducing the levels of the minor lobes of linear, rectangular, and circular radiators is considered theoretically. The shading is accomplished by using equiphase normal‐velocity distributions limited to two discrete amplitudes. Relationships are derived for the sound‐intensity directivity pattern and the directivity index of each radiator. An exhaustive study of various directional properties of such radiators is undertaken. This information is presented in terms of the behavior of the major‐lobe width, minor‐lobe levels, and directivity index as functions of (1) the ratio of the two normal‐velocity amplitudes and (2) the fraction of the unit having the higher source amplitude. It is shown that linear and rectangular radiators with such source distributions can be designed so that all minor‐lobe levels are at least 21 decibels lower than the major‐lobe level; the corresponding value for the circular radiator is 28 decibels. The resultant increase in major‐lobe width is approximately twenty percent. The results are presented so as to provide criteria for the effective use of this method in transducer design.

Design and Performance of a High‐Frequency Electrostatic Speaker

Lloyd Bobb, R. B. Goldman, and R. W. Roop

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1128-1133 (1955); (6 pages)

Online Publication Date: 29 Jun 2005

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An electrostatic speaker has been developed which provides a high quality of high‐frequency reproduction not available with electromagnetic tweeters. The diaphragm consists of a thin plastic film bearing an evaporated metallic layer. The membrane is stretched around a semicylindrical perforated electrode on which ridges are embossed to provide clearance. The response varies less than ±2 db in the frequency range between 8 and 16 kc. The azimuthal distribution pattern is excellent, owing to the cylindrical geometry, and is essentially independent of frequency in the same range. The second harmonic distortion inherent in this type of speaker is maintained at a low value. An indication of the quality of high‐frequency reproduction is provided by oscillograms of the response to tone burst signals. The speaker is in quantity production and has been incorporated in several models of home reproduction instruments.

Probe Microphone Analysis and Testing at High Temperatures and High Intensities

Kenneth W. Goff and Derwent M. A. Mercer

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1133-1141 (1955); (9 pages)

Online Publication Date: 29 Jun 2005

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A probe microphone has been developed suitable for measuring sound fields within such structures as altitude wind tunnels and jet engine test cells. This paper describes the methods of testing and analyzing the instrument. The microphone consists of a ⅜‐in. inside diameter probe tube with a porous metal tip, a condenser microphone, and a spiral resistive termination. It operates at sound‐pressure levels up to 170 db with 2% distortion, at ambient pressures down to 0.2 atmosphere, and with probe tip temperatures up to 900°F. The normal incidence response is flat within ±3 db from 10 to 10 000 cps.
An electrical analog of the acoustical system is given as a basis for explaining and predicting the performance of the microphone under varying ambient conditions. It appears that the microphone can be used satisfactorily as a cavity terminated probe microphone for frequencies below the frequency at which the spiral termination ceases to be “anechoic.” The required length of the spiral termination is then determined by the probe‐tube length rather than the lowest frequency of interest.
Testing methods and apparatus are discussed, including a high‐temperature flow resistance apparatus, a low‐pressure test chamber, and a resonant tube device for developing sound pressures up to 175 db with low distortion.

Mechanical Mechanism of Destructive Effects of Sound on Tissue

Walter Welkowitz

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1142-1144 (1955); (3 pages)

Online Publication Date: 29 Jun 2005

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A mechanical mechanism is presented to explain some of the nonthermal, noncavitation effects of high‐intensity sound on tissue. The theory proposes that the observed effects result from unidirectional forces produced by the acoustic wave, and that these forces cause elastic failure in the system. Some experimental verification is presented from measurements on irradiated frog muscle tissue and on irradiated frog spinal cord.

Effects of Noise on the Blood‐Eosinophil Levels and Adrenals of Mice

Adam Anthony and Eugene Ackerman

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1144-1149 (1955); (6 pages)

Online Publication Date: 29 Jun 2005

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Physiological changes are described following exposure of mice to single and intermittent noise stimulation (110 db re 0.0002 dyne/cm2, 10–20 kc) for varying lengths of time. Attention is focused on the degree of adreno‐cortical activation as measured by cytological changes in the adrenal gland and fall in the number of circulating eosinophils. Since the observed changes were transient, of short duration and no evidence of systemic pathology could be detected, the noise was described as not harmful. The tendency of certain investigators to regard noise as an injurious, nonspecific stress stimulus without specifying the exact nature of the noise situation does not seem justified.

Effects of Noise on Eosinophil Levels of Audiogenic‐Seizure‐Susceptible and Seizure‐Resistant Mice

Adam Anthony

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1150-1153 (1955); (4 pages)

Online Publication Date: 29 Jun 2005

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The occurrence of a diurnal rhythm in circulating eosinophils is described in mice selected on the basis of susceptibility to sound‐induced audiogenic seizures. Daily exposures of seizure‐susceptible and seizure‐resistant mice to single, short noise bursts for 30 days does not abolish or alter this rhythm, provided a recovery period is allowed between the last stimulation and the time of blood sampling. A single noise stimulus is followed by a moderate eosinopenia seizure‐resistant mice and a marked eosinopenia in seizure‐susceptible mice in about 3 hours; recovery occurs in both cases within 24 hours. A prolonged eosinopenia occurs with several successive noise bursts—at a moderately low level (ca 250 eosinophils/cu mm blood) in seizure‐resistant mice and at lower levels (ca 100 eosinophils/cu mm blood) in mice which experience convulsions during treatment. It was concluded that noise stimulation acts as a mild stress stimulus and is harmful only when it results in the production of fatal convulsions.

Design and Testing of Earmuffs

J. Zwislocki

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1154-1163 (1955); (10 pages) | Cited 1 time

Online Publication Date: 29 Jun 2005

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Factors controlling the sound attenuation provided by earmuffs are analyzed and an upper limit is estimated of the attenuation that can be expected from simple earmuffs without sacrificing comfort. Further discussion concerns the best dimensions of the earmuff and what can be achieved by adding one or more Helmholtz resonators.
The sound attenuation provided by two different earmuffs was determined on eight subjects in three sessions with a Békésy audiometer. The experimental procedure is described in detail and the results are analyzed statistically. Special attention has been paid to the changes in the listener's threshold of audibility with increasing experience.

Mechanical Impedance of the Forehead and Mastoid

Edith L. R. Corliss and Walter Koidan

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1164-1172 (1955); (9 pages) | Cited 1 time

Online Publication Date: 29 Jun 2005

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A method has been developed for determining the resistive and reactive components of the impedance of the human head and mastoid, or of other high mechanical impedances, using a special direct‐recording measuring system that records both force and motion. Impedances presented to driving tips of 12.5 and 20 mm diameter have been measured over the audio‐frequency range from 40 to 10 000 cps. The effects of static force coupling the head to the driver have been compared for 500‐ and 1000‐g coupling forces. Over a large part of the audio‐frequency range, the predominant characteristic of both head and mastoid impedance is a stiffness reactance, with some damping. In the high‐frequency range, a small mass reactance parameter appears. The mass load due to the whole head influences the impedance only at the low‐frequency extreme of the measurement range.
The driving system consisted of a tubular section of polarized barium titanate, rigidly clamped at one end to a massive wall. Force and motion were measured close to the point of contact with the lead, to minimize errors arising from flexure in the driver or between the sensing elements. The system was calibrated by loading the driving tip with known masses.

Rating Scale Method for Comparative Loudness Measurements

Walter C. Michels and Beatrice Taylor Doser

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1173-1180 (1955); (8 pages)

Online Publication Date: 29 Jun 2005

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A recently developed method for the use of comparative rating scales in psychophysical measurements has been applied to loudness judgments. It is found that the theoretical predictions are verified to within the experimental accuracy but it is indicated that the method is subject to certain limitations, which prevent complete verification of the theory. The values of the various undetermined parameters which enter into the prediction of judgments have been determined. It is found that the self‐adaptation in hearing is large (80%), and that the effects of residual stimuli and of other stimuli than the standard or the stimulus being judged are extremely small.

Absolute Pitch

A. Bachem

J. Acoust. Soc. Am. Volume 27, Issue 6, pp. 1180-1185 (1955); (6 pages) | Cited 5 times

Online Publication Date: 29 Jun 2005

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The author, who possesses absolute pitch since the time of his earliest musical experiences at the age of five years, has spent much time in studying this musical phenomenon. Amused by the fact that the most extensive work on “absolute pitch” was conducted by psychologists who did not possess this faculty and that it was done on large groups of students, none of whom possessed this faculty either [For exception see O. Abraham, Sammelbde d. Internat. Musikges 3, 1 (1901) and G. Révész, Zur Grundlegung der Tonpsychologie (Leipzig)], he was convinced that a study by a possessor of absolute pitch on himself and on a large number of other possessors of absolute pitch might lead to different and better results. An original study [A. Bachem, J. Acoust. Soc. Am. 9, 146 (1937)] was conducted on 96 possessors of absolute pitch and 7 more or less musical persons without this faculty for comparison. The work was extended in the course of time to specific related problems which presented themselves through several discoveries.
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