Volume 26, Issue 6, November 1954

Twenty‐Five Years of Musical Acoustics
View Description Hide DescriptionTwo highlights of musical acoustics of the past twenty‐five years are the advent of practical electrical musical instruments and research on deviations from the regular in music. Included in the latter are studies of the vibrato, transient modifications of tone quality, departures of intonation from rigid scales. The “steady‐state” concepts of the past now need refurbishing in the light of “deviation” evidence. An analysis of papers directly related to music and published in the first twenty‐five volumes of the Journal of the Acoustical Society of America reveals a steadily increasing interest in musical acoustics until World War II. In common with other subjects the publication rate dropped sharply during the war. Publication in acoustics as a whole increased rapidly after the war, but interest in musical acoustics (at least as evidenced by papers in the Journal) did not revive. Patents on musical devices, however, now constitute a significantly larger percentage of the annual output of the U.S. Patent Office than was the case in 1941. Technology is outstripping research in musical acoustics; interest in research must be revived immediately for the benefit of those who will listen to music in the next twenty‐five years.

The Transient Tones of Wind Instruments
View Description Hide DescriptionOscillograph records of the initiation of sound in organ pipes and orchestral wind instruments show large variations from one instrument to another. The causes of these variations and their artistic effects are discussed.

Electronic Pulse Method for Measuring the Velocity of Sound in Liquids and Solids
View Description Hide DescriptionA pulse method is described employing a “sing around circuit” wherein each new pulse is triggered by the preceding pulse after it has traversed the acoustic sample. The resulting pulse repetition rate is measured with an electronic stop watch, thus giving a measure of the combined acoustic and electronic delay times. This in turn, upon the elimination of the electronic delay time, gives the velocity of sound in the sample. Velocity data are presented and sources of error discussed.

Ultrasonic Absorption in Acetate Solutions
View Description Hide DescriptionThe amplitude absorption coefficient α for continuous ultrasonic waves in aqueous solutions of copper acetate, sodium acetate, and potassium acetate has been measured over a range of frequency from 7 to 45 mc, at temperatures between 5° and 50°C, and at concentrations up to 0.5 M. The experimental values for copper acetate solutions confirm the existence of a relaxation frequency at about 18 mc (at the higher concentrations). The results for sodium and potassium acetate solutions show an absorption coefficient below that of pure water at the higher frequencies. They also indicate the existence of relaxation frequencies below 10 mc.

Theoretical Investigation on the Diffraction of Light by Superposed Ultrasonic Waves
View Description Hide DescriptionAn analytical treatment for the calculation of intensities of diffraction orders in a general case of superposed sound waves of frequencies in the ratio 1 :n and having any phase difference Δ is given proceeding from Raman and Nath's simplified theory for normal incidence. Because of the integral harmonic relationship between the frequencies of the sound waves superposed, a particular order may contain a number of combination lines in addition to the orders due to the individual sound waves. As such, Fues theory, which gives a single expression for the intensity of a combination line, cannot be applied to this case.
Expressions are obtained for the intensities of the diffraction orders in the two specific cases of even and odd values of n. In the case diffraction by two sound waves of frequencies in the ratio expressions for the intensities of the orders suggest symmetry in diffraction for all values of Δ. But, when the superposed frequencies are in the ratio 1:2k, the expressions suggest asymmetry in diffraction for all values of λΔ, except π/2. When Δ = π/2, the diffraction is, however, symmetric.
Using the expressions, the intensities of the diffraction orders obtained by two sound waves of frequencies in the ratio 1:3 superposed in three different phases 0, π/2, and π are calculated for the values of and , 2, and 3.

Frequency Dependence of Ultrasonic Cavitation
View Description Hide DescriptionOn the basis of a simplified model an explanation for the high‐frequency limit of ultrasoniccavitation is suggested and compared with published experimental data.

Measurement of High‐Frequency Sound Velocity in Mammalian Soft Tissues
View Description Hide DescriptionA two crystal interferometer for rapid measurement of soundvelocity in liquids and soft animal tissues is described. Velocities can be determined to within three parts per thousand with a path length of a few millimeters. The frequencies used are 1, 2, 4, 12, and 36 mc. Temperature is controlled to 0.1°C. A phase comparison method is used for wavelength incorporating dual heterodyne reduction to audio‐frequency with presentation as a Lissajous figure on an oscilloscope. Results are given for a few mammalian tissues showing the precision and reproducibility of measurements.

Gas Bubbles with Organic Skin as Cavitation Nuclei
View Description Hide DescriptionThe hypothesis discussed that the cavitation nuclei consist in gas bubbles. Due to surface tension, small bubbles would dissolve in a very short time. If the bubbles are larger than , or if the liquid is supersaturated, they may last longer or even be stable, but then no cavitation threshold exists.
The hypothesis expressed that the nuclei are very small bubbles, stabilized by an organic skin, which mechanically prevents loss of gas by diffusion. The cavitation occurs when the skin breaks and the threshold is determined by the breaking strength of the film and the size of the bubble.

Conductivity and Viscosity Effects on Wave Propagation in Piezoelectric Crystals
View Description Hide DescriptionThe effect of electrical conductivity and viscosity of the piezoelectric medium propagating plane waves has been studied. The solution of Maxwell's field equations and Newton's law of force in the general medium gives the modified elastic,piezoelectric, etc., constants necessary for determining the phase velocities of the plane waves. These modified constants are found to be complex and frequency dependent. Thus the propagation constants for the waves are complex and frequency dependent.
A particular example, propagation in the 1‐direction of ammonium dihydrogen phosphate, is considered.

Absorption of Finite Amplitude Sound Waves
View Description Hide DescriptionThe coefficients of absorption of high intensity ultrasonicwaves in liquids (carbon tetrachloride and water) have been measured as a function of intensity. The absorption coefficient increases by a factor of 5 for water and 2 for carbon tetrachloride for intensities of about . The increase is attributed to wave form distortion of a wave of finite amplitude. A theory is developed in which the medium is treated as the acoustical analog of a transmission line with nonlinear elements. The theory enables one to follow the details of the change of an initially sinusoidal wave of finite amplitude, in a dissipative medium, in to a “comparatively” stable distorted wave form that eventually returns to an infinitesimal sinusoidal wave. Quantitative agreement of theory is obtained with experiment for the distance needed for comparative stabilization, the growth of harmonic content in the distorted wave, and the details of the absorption process.

Acoustical Streaming in the Vicinity of a Cylinder
View Description Hide DescriptionApparently contradictory reports in the literature concerning the acoustic streaming around a right‐circular cylinder immersed in a viscous, incompressible fluid can be reconciled by reference to a universal curve giving (δ _{DC}/a) as a function of (a/δ_{ AC }), where δ_{ DC } is the DC boundary‐layer thickness, δ_{ AC } is the AC boundary‐layer thickness, and a is the radius of the cylinder. The existence of such a curve has been verified experimentally for the case of a right‐circular cylinder vibrating to and fro in solutions of water and glycerin with kinematicviscosities ranging up to 50 times that of water, over an octave of frequencies. This experimental work also confirms theoretical predictions that for small oscillation amplitudes the streaming patterns will be the same whether the cylinder oscillates in a quiescent fluid or is fixed in an oscillating fluid. An approximate equation for the form of the universal curve has been obtained theoretically for the case of a thin AC boundary layer, when the oscillation amplitude is small enough to insure the validity of a first‐order perturbation solution. Preliminary results of experimental work at higher amplitudes are reported, and the effect of the compressibility of the fluid on the streaming is discussed.

Dispersive Reflection at the Interface between Ideal and Viscous Media
View Description Hide DescriptionThe effects of viscosity and heat conduction (in the reflecting medium) in producing dispersive reflection of a plane wave at the plane interface separating two media are investigated. If the reflecting medium is treated as a condensed fluid, heat conduction is found to have no effect, while, in first approximation, viscosity is found to produce no change in amplitude but a phase shift proportional to frequency (and therefore no phase distortion) at angles of incidence above critical and to produce no phase shift but amplitude distortion at angles below critical. This amplitude distortion is found to be important only in the neighborhood of a sharp wave front.

Compressional Waves along an Anisotropic Circular Cylinder Having Hexagonal Symmetry
View Description Hide DescriptionExact solutions are derived for the propagation of compressional elastic waves along an anisotropic circular cylinder having axial elastic symmetry (hexagonal elastic symmetry with the crystallographic axis coincident with the cylinder axis). Formal solutions are obtained for the displacement components, and a transcendental equation relating the phase velocity and the circumference‐to‐wavelength ratio is derived. The solutions are shown to reduce to the Pochhammer solution for the isotropic case. In the long wavelength extreme the velocity is dispersionless and is given in terms of the axial Young's modulus. In the short wave‐length limit the velocity again becomes constant, similar to the Rayleigh surface wave limit in the isotropic case.

Air‐to‐Ground Sound Propagation
View Description Hide DescriptionThe attenuation of sound in air, in the vertical direction, has been measured on six occasions using an aircraft flying at various heights over a microphone at ground level. It was found that there was always negligible attenuation at frequencies below 1000 cps even though the air was turbulent; at higher frequencies the attenuation was found to be of the same order as the Knudsen‐Kneser results for attenuation due to molecular absorption.

Acoustical Studies of the Tractrix Horn. I
View Description Hide DescriptionWhen predicting and comparing the acoustical properties of horns it is customary practice to formulate the propagation as a one‐parameter plane wave front problem. However, when particular attention is paid to the rapid flare near the mouth of a horn structure such as the tractrix, it also seems plausible to formulate the propagation on the basis of a one‐parameter spherical wave front theory. By visualizing the surfaces of constant phase as spheres of constant radii a and the flow lines as tractrixes having a generating arm of length a, a one‐parameter wave equation and Ricatti impedance equation may be derived. Solutions to these equations have been obtained by waveperturbation and by analog computer techniques.
Axial response and throat impedance measurements are compared with theoretical calculations postulating first a hemispherical and then a plane piston radiation pattern. It appears that the most satisfactory explanation lies somewhere in between these two limiting cases.

Acoustical Studies of the Tractrix Horn. II
View Description Hide DescriptionExperimental investigations have been carried out on the tractrix horn structure to determine its “free‐field” radiation characteristics. Axial, off‐axis, and polar response characteristics, as well as throat impedance data on a single cell horn, are presented for both small and large baffle mounting. Pertinent data on a two cell structure are also presented. These data show the tractrix performance to be comparable with that of the well‐known exponential horn. A multicellular structure, while showing definite improvement in uniformity of angular distribution at high frequencies, exhibits undesirable band rejection characteristics within the useful frequency range of the horn.

Maximum Directivity Index of a Linear Point Array
View Description Hide DescriptionThe maximum directivity index of a symmetrical, linear point array has been calculated as a function of the number and spacing of the elements in the array. The excitation required to produce a maximum directivity index is not uniform, except for integral‐half‐wavelength element spacings, and in general the minor lobes of the directional response patterns produced are not of equal, nor of small, amplitude. For element spacings exceeding a half‐wavelength, a conventional type of pattern and of excitation is found to produce the maximum directivity index. On the other hand, as the element spacing is reduced below a half‐wavelength, the directivity patterns corresponding to the maximum directivity index become super‐directive, and the directivity index may be improved relative to the value obtainable with uniform excitation. However, this improvement is obtained only at the expense of requiring large, reversed‐phase excitation. Numerical results are presented for 3‐, 5‐, and 7‐element arrays.

Experimental Investigation of Wedge Horns Used with Line Hydrophones
View Description Hide DescriptionA study has been made of wedge‐shaped horns used in conjunction with line sources. The horns are constructed from aluminum plates covered with cellular rubber. Measurements were made over the frequency range of 60 kc to 150 kc using horn lengths from 3 inches to 15 inches and horn angles up to 90 degrees. Results are given graphically in the form of directivity patterns as well as relative gain in sensitivity and beam widths as a function of the several parameters. At 80 kc beam widths as low as 10 degrees are obtained with at least 40 db suppression of the secondary lobes. The horns are easily fabricated and the beam width and sensitivity of the transducers are easily controlled by varying the horn angle.

Cumulative Effects of Repeated Bursts of White Noise on Threshold for 4000‐cps Tone Pips
View Description Hide DescriptionCumulative effects of a two‐second burst of thermal noise on the threshold shift for 35‐millisecond tone pips were examined by tracing the threshold shift over the course of 100 successive noise bursts. When bursts were presented at a rate of 6 per minute, a systematic increase in the threshold shift for the 35‐millisecond tone pip was observed over the 100 burst series. Changing the burst‐pip interval from 90 to 445 to 1000 milliseconds had little effect on the degree of this accumulation, but changing the SPL of the burst had a marked effect. At a burst level of 110 db (SPL re 0.0002 microbar) the mean threshold shift increased by about 6 db between the 15th and the 100th burst. Decreasing the burst level to 100 db reduced the mean accumulation to about 4 db, and at a burst level of 90 db to about 1 db. Changing the burst presentation rate from 6 per minute to 3 per minute reduced, but did not eliminate, the cumulative effect. The degree of this cumulative phenomenon showed wide individual differences among subjects.
It is concluded that, unless proper allowances are made, the repetitive stimulation required by burst‐pip audiometry may be a source of serious error. On the other hand, the reaction of an ear to repeated stimuli may prove to be a useful index of the ear's susceptibility to irreversible acoustic trauma.

Masking of Speech by Repeated Bursts of Noise
View Description Hide DescriptionThe masking of speech by a periodically interrupted white noise was examined over a wide range of noise levels, rates of interruption, and noise‐time fractions. To a first approximation, the masking produced by an interrupted noise is a constant fraction of that produced by a continuous uninterrupted noise. The masking produced by an interrupted noise is primarily a function of the interval between successive noise bursts and is relatively independent of the noise‐time fraction and the rate of interruption of the noise, except insofar as these determine the interval between noise bursts. The effect of interrupted noise on the loudness of speech was also examined.