Volume 24, Issue 1, January 1952

The Theory of Sound Absorptive Materials
View Description Hide DescriptionThis paper presents a review of the status of the theory of sound absorbing materials. The basic concept of absorption coefficient, as well as the relation between absorption coefficient and acoustical impedance are discussed. Other topics considered are, sound propagation in homogeneous isotropic media, perforated panels, suspended absorbers, and resonant absorbers.

A Precise Recording Ultrasonic Interferometer and Its Application to Dispersion Tests in Liquids
View Description Hide DescriptionA precise recording ultrasonicinterferometer is presented which is particularly well suited for measuringdispersion in liquids. The device is an interferometer of the two‐crystal type in which the separation of the crystals is continuously varied. The recording process is equivalent to placing a mark on a rotating recording drum whenever the receiving crystal has moved a distance of one wavelength of sound in the liquid. Thus the wavelength of sound may be derived from the known mechanical constants of the system. The precision of the dispersionmeasurement is about 0.8 part in 10,000; the precision of the absolute determination of sound velocity is 0.2 m/sec. The instrument has been applied also to sound velocity measurements in solids under restricted conditions.
Sound velocity in distilled water at 25°C as measured with this instrument is 1496.2±0.2 m/sec, a value somewhat lower than that obtained by earlier investigators.
Dispersion in the frequency range 5–25 Mc is shown to be no greater than 0.8 part in 10,000, the limit of experimental error, for all the liquids studied: water, geraniol, xylene, isobutyl alcohol, and solutions of sucrose, NaCl, , and .

The Absorption and Dispersion of Sound in Oxygen as a Function of the Frequency‐Pressure Ratio
View Description Hide DescriptionThe velocity and absorption of ultrasonicwaves in oxygen were measured by means of an improved ultrasonic interferometer in the range from one to one hundred Mc per atmosphere. Dispersion of the velocity ranged from 333.14 m/sec, to 357.22 m/sec at 30°C. The ratio (α_{exper}/α_{class}) dropped from 3.68 to 2.05, and the corresponding value of C_{v}/R dropped from 2.50 to 1.61. The increase in velocity and the decrease in (α_{exper}/α_{class}) is interpreted as caused by the slow exchange of energy between the translational and rotational degrees of freedom. The relaxation time for the rotation was 5.24×10^{−9} second.

On the Theory of the Fixed Path Acoustic Interferometer
View Description Hide DescriptionA general expression is given for the electric input impedance of the acoustic interferometer. From this expression formulas are derived for determining the velocity of sound by varying the frequency, or for determining changes in velocity due to variations of pressure, temperature, etc. In papers dealing with the fixed path interferometer, one commonly finds the suggestion that the actual path length needs some correction when the path ends at a nonperfect reflector. It will be shown that no such correction is indicated by the theory.

A Recording Ultrasonic Interferometer and its Alignment
View Description Hide DescriptionThe first part is the description of a circuit employing rf amplification which converts an ultrasonicinterferometer into a sensitive self‐recording instrument whose records can be simply analyzed to yield a rapid determination of the attenuation and reflection coefficients of gases at low pressures. The second part is a summary of the sources of error in ultrasonicinterferometry, their detection and their correction. In the third part, some data on the velocity,attenuation, and reflection in helium in the region two to sixty Mc/atmos are presented to illustrate the range, precision, and absolute errors of the instrument.

A Mechanical Shock Tester for Instruments and Electronic Apparatus
View Description Hide DescriptionA mechanical shock tester of the free‐fall type has been designed to produce high accelerations in the form of a square wave. The apparatus is described, and the logical considerations which were used as design parameters are explained. Particular attention is paid to the relation between the shocks an equipment is likely to receive in practice and the optimum type of test apparatus.

Attenuation of Sound in Water Containing Air Bubbles
View Description Hide DescriptionMeasurements of the attenuation of sound in water containing air bubbles were undertaken in order to confirm some aspects of a theory due to L. L. Foldy. Bubbles were produced by forcing compressed air through the cloth covering of several trays lying on the bottom of the Black Moshannon Lake. The distribution in size of the bubbles and the number of bubbles per unit volume were determined by photographing the bubbles and by collecting the volume of air which rose over a given area in a given time, the terminal velocity of rise being a known function of bubble diameter. The attenuation of sound was found to be very large at frequencies for which resonant bubbles were present, and much smaller at other frequencies, indicating that resonanceabsorption was the principal phenomenon observed. For the particular bubble distribution investigated, which contained 0.045 percent air by volume, the attenuation was found to be in satisfactory agreement with the theory and a maximum attenuation of approximately 20 db per inch was measured. Amplitude and phase fluctuations made it impossible to measure the phase velocity, but this quantity was computed from the bubble distribution.

Frequency‐Band Multiplication or Division and Time‐Expansion or Compression by Means of a String Filter
View Description Hide DescriptionA frequency band multiplication or division has been performed by string filters. An exact relationship between the input and output frequencies has been shown. Two different methods have been used.
The first multiplies frequencies by rectification with the aid of a push‐pull electrostatic pick‐up. Alternating plus‐minus polarizing techniques are employed to suppress the undesirable sum frequencies. The resolution of such a doubling system, which will not pass the sum frequencies, is approximately 1.5 times the band width of the single filters. However, the band width is limited by the transit time of speech.
The second method multiplies and divides by exciting the harmonics or subharmonics of the single strings. This is done by employing light, stiff “fingers” to disturb the free oscillations of the damped strings. The excitation and the resulting frequency band division and multiplication are investigated.
It is shown that in order to get time compression or expansion, it is only necessary to record the multiplied or divided frequency bands and play them back with the corresponding diminished or increased speeds.
The results given have a general application to similar type filters such as reed, crystal or magnetostrictive.

A Time Constant Meter for Tuning Forks and Other High Q Devices
View Description Hide DescriptionThe time constant meter described operates on the principle that differentiation of an exponentially decaying rectified envelope decreases it in inverse proportion to the time constant and reverses its sign. Hence, it is possible to obtain a null by balancing the differentiated signal against a portion of the original. The circuit is simple, requiring only one amplifier tube and a tuning eye.

Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders
View Description Hide DescriptionA formal solution in terms of cylindrical wave functions is obtained for the scattering of a plane acoustic or electromagnetic wave by an arbitrary configuration of parallel cylinders which takes into account all possible contributions to the excitation of a particular cylinder by the radiationscattered by the remaining cylinders. The solution, satisfying any of the usual prescribed boundary conditions simultaneously at the surface of each cylinder, is expressed as the incident wave plus a sum of various orders of scattering. The first order of scattering (the usual single scattering approximation) results from the excitation of each cylinder by only the plane wave or primary excitation. The second order results from the excitation of each cylinder by the first order of scattering from the remaining cylinders, and so on to an infinite order of scattering. The first order therefore consists of waves scattered by one cylinder; the second order of waves scattered by two cylinders, etc. The scattering coefficients of the m'th order of scattering are expressed recursively in terms of the previous orders, and finally as sums of products of mscattering coefficients of the single cylinder and Hankel and trigonometric functions depending on the geometry of the configuration.

Directionality Patterns for Acoustic Radiation from a Source on a Rigid Cylinder
View Description Hide DescriptionThe directionality patterns produced by an acoustic source located on a rigid cylinder of infinite length have been investigated for the case in which the source strength may be represented as a separable function of azimuth angle and axial dimension. It is observed that the pattern in a plane orthogonal to the axis of the cylinder is independent of the axial distribution of the source, and is, in fact, identical with the pattern given by Morse for a source of infinite axial extent. For the particular case in which the ratio of circumference to wavelength is 14, patterns in this plane have been computed numerically using an IBM Card‐Programmed Calculator. Patterns in a plane containing the axis of the cylinder have also been investigated.

The Design of Optimum Directional Acoustic Arrays
View Description Hide DescriptionA transducer array has been designed according to underlying theory originally applied to broadside electromagneticantenna arrays by Dolph. The properties of Tschebyscheff polynomials have been employed to obtain an optimized relationship between minor‐lobe level and main beam width.
The shading design of a 130 element circular array is carried out utilizing a distance between stack centers of 5λ/8. Experimental measurements of the resulting transducer give a peak sensitivity of −70 db below 1 volt for a field of 1 dyne per cm^{2}, 11 degrees main beam width at the 3‐db down points, and suppression of side lobes to more than 32 db below peak sensitivity.

The Free Vibrations of a Gas Contained within a Spherical Vessel
View Description Hide DescriptionNumerical values of the lowest 84 natural frequencies of vibration for the spherical acoustic resonator are calculated and listed in appropriate tables. Consideration is given to the geometrical structure of the nodal surfaces associated with each mode of vibration and to the degeneracy of each natural frequency.

The Modes of Vibration of a Semi‐Flexible Rod under Tension
View Description Hide DescriptionThe possible modes of vibration of a rod under conditions which are intermediate between a perfectly flexible string under tension and a stiff bar without tension have been calculated from existing theory. An experimental investigation of the first ten modes gave results in agreement with the theory within approximately 0.5 percent. Deviation from a harmonic series increases with the number of the mode of vibration, but is considerably less than for a stiff bar.

Wave Effects in Isolation Mounts
View Description Hide DescriptionBoth theoretical and experimental studies of wave effects in isolation mounts have been made. From the standpoint of vibration isolation, wave effects are important in the sense that the vibration isolating properties of a mount are changed by their presence. The well‐known “lumped parameter” theory of vibration mounts predicts that the vibration isolation of a mount increases at 12 db per octave for frequencies well above the resonant frequency of the spring‐mass system. This theory holds true only when the wavelength of the elastic wave in the mount is large compared to the dimensions of the mount. Standing waves occur, as would be expected, which in certain frequency ranges decrease the vibration isolation properties of the mount by as much as 20 db. For practical mounts, wave effects are most detrimental in the most audible frequency range (500 to 1000 cps). The theoretical and experimental treatments are in good agreement, and indicate various methods for improving the vibration isolation properties of the mount. Experimental data concerning isolation mounts fabricated of various materials are presented.

DC Resting Potentials Inside the Cochlear Partition
View Description Hide DescriptionInside the cochlear partition there is without any acoustical stimulus a dc potential difference between the organ of Corti and the endolymph of the order of 100 millivolts. The possible significance of this potential difference has been pointed out. The magnitude of the potential difference seems to indicate that the cochlear partition represents a pool of energy.

Frequency Discrimination for Damped Waves
View Description Hide DescriptionMeasurements of frequency discrimination for single damped waves are reported for frequencies between 200 and 5000 cps, and for values of the damping σ between 0 and 500 sec^{−1} (σ is the reciprocal of the time constant of the envelope of the damped wave). There is an increase in the difference limen for frequency as the damping increases, or as the effective duration decreases. The increase in the difference limed is accompanied by a loss in the pitch character of the stimulus, and there is usually a sharp deterioration in discrimination above a certain value of damping, i.e., above a certain band width of the stimulus. The results are related to existing data on the perception of short sinusoidal stimuli.

A Loudness Chart for Octave‐Band Data on Complex Sounds
View Description Hide DescriptionThe equivalent‐tone method of Beranek, Marshall, Cudworth, and Peterson has been used as a basis for developing a loudness chart for octave‐band data on noise. The loudness chart consists of contours of equal pressure level in octave bands which are superimposed on a loudness grid. The procedure is based on octave‐band data, since octave‐band filter sets are readily available commercially and are being widely used in noise measurement. Good agreement is shown with loudness values for various noises determined by Beranek et al., using 300 and 600‐mel bands, and there is, therefore, good agreement with existing psychological data. The loudness chart not only facilitates the calculation of loudness but provides graphical loudness curves for comparison of noise and for the evaluation of various noise reduction measures.
 LETTERS TO THE EDITOR


Acoustical Energy Generated by the Ocean Waves
View Description Hide DescriptionAn estimate of the order of magnitude of the acoustical energy generated by ocean waves indicates that this energy, is large enough to cause an appreciable heating effect at ionospheric levels, where most of it is absorbed. Using data obtained from surface measurements of the pressure amplitude, it is found that relative density changes of the order of 1 percent occur at ionospheric levels. and the suggestion is made that the “twinkling” of cosmicsources of radio waves is a result of this phenomenon.

Radiation Impedance of a Rigid Square Piston in an Infinite Baffle
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