Volume 32, Issue 12, December 1960

Frequency Response of a Nonlinear Stretched String
View Description Hide DescriptionThe problem of the forced vibration of an elastic string with variable tension is considered. All equation of motion is given for the case of low amplitude motion, but for strings of high modulus for which it is shown that tension variations are an important source of nonlinearity. An exact solution is obtained by assuming as a driving function a Jacobean elliptic function of the cosine type. Tension variations and amplitude are calculated as functions of frequency. Experimental results are presented and compared with the theory.

Dynamics of a Hollow, Elastic Cylinder Contained by an Infinitely Long Rigid Circular‐Cylindrical Tank
View Description Hide DescriptionDispersion equations are derived for the propagation of transverse waves within an infinitely long thick‐walled hollow elastic cylinder which is perfectly bonded along its outer cylindrical surface to an infinitely long rigid circular cylindrical tank. In the case of infinite wavelength the dispersion equations reduce to two uncoupled frequency equations; one defining the natural frequencies of free vibrations of the hollow elastic core in the antisymmetric axial shear mode and the other defining the natural frequencies of plane strain vibrations. Some numerical results are presented for the dispersion equations and the two frequency equations and references are given to more detailed results.

Fluctuations of Sound Reflected from the Sea Surface
View Description Hide DescriptionExperimental data on the reflection of sound from the sea surface suggest that the fluctuations of the received signals are due to the scattering of sound from the irregular sea surface. These data are compared with calculations based on the theory of Eckart. A Gaussian correlation function for the sea surface was assumed for the calculations. The scatteredsound depends upon the sea surface parameters, source position, receiver position, and acoustic wavelength. The numerical calculations of scatteredsound had the same dependence on the source‐receiver separation as the experimental data. By using this, the correlation distance and rms wave height are estimated for the sea surface.

Fluctuations in Surface‐Reflected Pulsed cw Arrivals
View Description Hide DescriptionA pulse of 168‐cps sound was scattered from the ocean surface and analyzed for fluctuation as a function of the angle of incidence. A (cosφ)^{2.5} relation is found between the relative standard deviation of the energy and the incident angle, as measured from the normal.

Determination of Sound Absorption Coefficients Using a Pulse Technique
View Description Hide DescriptionA pulse method of determination of sound absorption coefficients using a sound mirror to produce directed sound pulses allows determination of the coefficients by essentially a free field method but within the confines of an ordinary laboratory. Average pulse pressures for brief pulses are obtained over both space and time to allow evaluation of the absorption coefficient as a function of angle of incidence. When averaged over angle of incidence, this function leads to an average absorption coefficient. Average coefficients were obtained for samples of two different materials. These coefficients, for a pulse two cycles long at 2000 cps, are 0.56 and 0.182. Comparable values computed from impedance tube data are 0.57 and 0.186; and values obtained from reverberation chamber measurements are 0.57 and 0.130. In each case the three values for each material lie within the estimates of error assigned. It is concluded that while the pulse method is confined to short pulses having relatively wide frequency spectra, the method is useful both in producing values of sound absorption coefficients as a function of angle of incidence and of average values of these coefficients.

Measurement of Perstimulatory Auditory Adaptation
View Description Hide DescriptionThe most frequently used estimate of perstimulatory auditory adaptation to a tone sustained in one (experimental) ear has been the intensity decrease at the contralateral (control) ear required for median‐plane localization during successive 15‐sec comparison intervals. Use of such a measure assumes that only negligible adaptation occurs in the control ear during these 15 sec. The results of this investigation show this assumption to be untenable. Adaptation in the control ear was measured by maintaining the experimental ear in an adapted state and then sustaining the comparison stimulus in the control ear. As the control ear adapted, the phantom sound associated with the tones to both ears moved toward the median plane. The time for this moving phantom sound to reach the median plane varied with the intensity and frequency of the comparison stimulus. The extent and rate of adaptation in the control ear was found to be such that all estimates of adaptation to tones sustained in the experimental ear are specific to the procedures used.

Psycho‐Acoustics, Applied and Misapplied
View Description Hide DescriptionThe paper is a historical survey of the attempted application of psycho‐acoustic phenomena during and immediately after World War II.

Scaling of Pitch Intervals
View Description Hide DescriptionA literature review showed that in bisecting a musical interval Ss tend to yield the arithmetic mean if the interval is large, but the geometric mean if the interval is small. Since fractionation judgments (“half‐pitch”) front which pitchscales may be derived would typically utilize quite hide intervals, and thereby tend to yield the arithmetic mean, a major discrepancy has arisen between such pitchscales and the pitchscale of our musical heritage, which is based upon the principle of the geometric mean. A number of experiments were performed using half‐pitch and bisection judgments, and several variants of the method of equal appearing intervals. From these it was concluded that when equal appearing interval judgments are used with a standard interval no larger than about a musical third, a reliable psychologicalpitchscale emerges which agrees well with the common pitchscale of the piano keyboard. However, if the standard interval is as large as a musical fifth, the pitchscale begins to tend toward that derived from fractionation.

An Air Damped Artificial Mastoid
View Description Hide DescriptionAn air damped artificial mastoid has been constructed to simulate the mechanical impedance of the human mastoid. Viscoelastic substances extensively used in current mastoid designs are not employed. The instrument is virtually immune to aging effects and can be easily reproduced. The instrument is used as a laboratory standard to determine the force transmitted through the skull by bone vibrators used in clinical audiometers and bone conduction type hearing aids.

Post‐Tetanic Potentiation in the Middle‐Ear‐Muscle Acoustic Reflex
View Description Hide DescriptionTemporary improvement in the threshold of the middle‐ear‐muscle reflex in response to sound occurs following short exposures to moderately loud sound (80–90 db). Pre‐ and postexposure reflex thresholds for several frequencies were obtained from awake cats with permanently implanted electrodes in the tensor tympani and stapedius muscles, and on the round window. The increased threshold sensitivity observed (up to 40 db) is considered to be classifiable a phenomenon of post‐tetanic potentiation, and as a demonstration of hyperexcitability in certain brain‐stem auditory structures following sound stimulation.

On the Mathematical Theory of Woodwind Finger Holes
View Description Hide DescriptionThe acoustical effects of open and closed finger holes on woodwind bores in the lower two playing registers are investigated in a mathematical formulation which permits a coherent and comprehensive understanding of the interaction of holes with the bore of a woodwind. Results are expressed in a way which permits accurate engineering calculation of all effects which are discussed. It is shown that when the holes are closed at their outer ends, the system is simply and accurately representable by an adaptation of standard transmission line theory for a tube with side branches. Interestingly, this representation is only possible for musically usable hole sizes and spacings. A related formulation is also possible for a sequence of open finger holes: once again the accuracy of the formulation is greatest for musically usable holes. The part of a woodwind bore that is provided with closed side holes functions as a low‐pass filter. Similarly the open holes lower down on the bore function as a high‐pass filter. The positions of both cutoff frequencies depend end critically upon the hole sizes and spacings. Both fall at frequencies which allow them to play a role in the tune production. Methods are given for calculating “end corrections” for bores with some open and some closed holes as well as for bores with perturbations to the bore cross section. The effects of “misplaced” or “mis‐sized” holes are investigated by these methods, and the position of the lowest open hole calculated. An estimate of the errors in these calculations shows them to be essentially exact for musical purposes. The radiation behavior of a row of open finger holes is analyzed. Frequencies below the “cutoff” of the open hole system are radiated essentially isotropically, while each of the higher components is emitted with its own pattern, all of which are roughly conical, in analogy with the shock wave produced by a supersonic projectile. The musical implications of this are discussed briefly. Light is shed on the function of the bell on woodwind instruments, and on the reason why a bell is not needed on certain of them. The dominant rule of the “closed hole” properties of a bore with finger holes is stressed throughout the paper.

Concerning the Noise of Turbulent Jets
View Description Hide DescriptionThe suggestion that the noise generators of turbulent jets undergo convectioneffects which are limited in such a way as to follow a similarity behavior leads directly to a resolution of Lighthill's paradox, namely, the problem of accounting for the noise power depending upon the eighth power of the jet velocity simultaneously with the gross directional bias. This hypothesis shown to be at least plausible to a first approximation owing to the general velocity field of the jet having typical dimensions comparable to a fraction of a wavelength; an important corollary is the expectation of appreciable refraction effects. Aspects relevant to the directional peaks of the higher frequencies being less pronounced and located further from the jet axis, and of the slow frequency rise, are briefly discussed.

Analog Measurements of Sound Radiation from the Mouth
View Description Hide DescriptionFree‐field measurements of the sound radiated from the mouth of a life‐size mannequin are described. A transducer installed in the head of the dummy is calibrated to produce a known acoustic volume velocity at the lips. The sound field in vertical and horizontal planes through the head is explored with a pressure microphone.Measurements of pressure magnitude and phase are made for frequencies of 250, 500, 1000, 2000, and 4000 cps. The results are compared with the sound distributions for a simple spherical source, and for a small piston in a sphere of 9‐cm radius. Over the frequency range investigated, and within a solid angle of about π sr centered on the mouth axis, the relations for the simple source are found to describe the measured magnitudes within approximately 3 db, and the measured phases within approximately 30 deg. The results are also compared with previously reported pressure distributions for speech. Some brief comment is devoted to approximating the radiation impedance of the mouth.

Speech Processing by the Selective Amplitude Sampling System
View Description Hide DescriptionSelective amplitude sampling is a speech processing technique in which the input speech waveform is sampled at the times of its maxima and minima. The original wave is reconstructed from its samples by means of a box‐car circuit followed by suitable filtering. The maxima and minima are determined from the zero crossings of the differentiated speech wave. Center clipping is employed to provide amplitude discrimination and a reduction in the average sampling rate. The intelligibility of speech processed by the system is compared with that for clipped differentiated speech and the original speech. “Quality” tests attempted to measure the ability of listeners to distinguish between words processed by the selective amplitude sampling system and a system in which the original words were filtered to a pass band of 300 to 3000 cps. Distributions were obtained of the sampling role averaged over 1‐ and 10‐sec intervals. Word intelligibility and sampling rate are also related to the degree of center clipping in the sampler. The degree of center clipping is measured in terms of an rms voice to‐threshold ratio. The word intelligibility scores on the selective amplitude sampling system had a mean of 93.8% and a standard deviation of 4.3%. In addition, 97% of all the test scores were equivalent to 100% sentence intelligibility. The results of the “quality” tests indicate that at least 36% of the time, the listeners were unable to distinguish between the selective amplitude sampling system and the filtered system. The average sampling rate necessary for 100% sentence intelligibility is approximately 1600 samples/sec. This rate corresponds to an rms voice‐to‐threshold ratio of 7 db.

Application of Cell Models to the Determination of Relaxation Times in Kneser Liquids
View Description Hide DescriptionThe vibrational relaxation times of several simple substances in the gaseous and liquid state are compared with values predicted by a simple cell theory of the liquid. Apart from some scatter of the experimental data, satisfactory agreement is found with the theoretical predictions.

Ultrasonic Attenuation in S.A.E. 3140 and 4150 Steel
View Description Hide DescriptionThe attenuation of longitudinal ultrasonicwaves from 5 to 95 Mc is studied by the pulse technique in blocks of S.A.E. 3140 and 4150 steel to determine the loss mechanism and to find possible methods for precision testing the microstructure of materials. It is found that scattering by the grains in the polycrystalline steel is responsible for the attenuation in tempered structure. The critical quantities are the grain diameter and the average squared fractional variation in the elastic modulus of a single grain. It is found that the attenuation is given within experimental limits in the case of steel with martensitic structure by the expression for Rayleigh scattering derived by Mason and McSkimin for the case of the wavelength much smaller than the grain diameter and by the expression for stochastic phase scattering derived by Huntington for the case of the wavelength to grain diameter ratios between and 3. The value of the average squared fractional variation in the elastic modulus (entering both expressions to the first power) was the one given by Mason and McSkimin for iron crystals. Bainite appears to have a higher value of this quantity. An alternative theory by Lifshits and Parkhomovskii may explain bainite. Tempering removed an elasticity from quenched structures. Suggestions for the exact solution for the attenuation at all frequencies are made, and methods of materials testing to investigate grain size and grain quality are outlines. Diffraction corrections and other items relevant to ultrasonic attenuation measurements are mentioned.

Theory of Sound Propagation through Ducts Carrying High‐Speed Flows
View Description Hide DescriptionThe important problem of sound propagation in ducts carrying compressible subsonic flows is analyzed on the basis that the motion is one‐dimensional. The multiple reflection method is extended to the case of sinusoidally varying pressure waves and a general integral formulation is developed. It is complicated because the total reflected wave, particularly, and the total transmitted wave must depend upon the time delay incurred by the propagation of infinitesimal reflections from along the length of the duct, and this depends upon the shape of the duct. It is shown how certain exact solutions can be obtained and these are given for the wave strengths composed of wavelets having undergone single, double and triple reflections. The frequency plays the strongest role in the reflected wave, and when the singly reflected wavelets dominate, it introduces a factor on the zero‐frequency reflection, Ω being proportional to the frequency, and it and χ being dependent upon the change of Mach number at the ends of the duct. In contrast the transmitted wave is hardly affected by frequency. The analytical results apply to “almost conical” ducts, either convergent or divergent with the incident wave propagating with or against the flow direction. An approximate method, based upon the analytical results is demonstrated for ducts of other form.

Outline of the History of Flexible or Elastic Bodies to 1788
View Description Hide DescriptionWhile several writings purport to give the history of elasticity and vibration, they are so inaccurate or fragmentary as to imply a general picture of the beginnings of these subjects that is outright false. A new history to 1788, drawn from detailed study of all the available sources, is to be published [C. Truesdell, The Rational Mechanics of Flexible or Elastic Bodies, 1638–1788, Leonhardi Euleri Opera Omnia (Ser. II, Vol. 11, Part 2, to appear in 1960)]. The present article provides a list of some of the specific discoveries described therein. The following pages may not conform to the reader's preconception of the subject, or to his idea of what the history of science ought to be. By a one‐sided selection of material, or by concentration on a particular problem such as that of the vibrating string, it would easily be possible to write a more inspiring tale of continued progress, or a case study in the development of science. Such a tale, such a study, even if correct in facts would serve only to reinforce all too widely received false pictures not only of how science developed but also of what science is. The problems whose history is outlined here were studied in interrelation to one another, not without steps sideways or even backward, and knowledge concerning them was not gotten in what now seems a logical order of development. This outline is intended for a reader already familiar with the modern theories of elasticity and vibration and already interested in their historical origin; its purpose is to answer for such a person questions of a kind most frequently directed to me, namely, “Who first discovered A?” and “What did B do for acoustics?” It is not, it cannot be a history of the subject. History cannot be understood from precis or digests, however accurate. The reader who desires consecutive explanations, equations, figures, and references may find them in my book. If I were to draw any summary moral from this development, it would be that mathematics was a more powerful tool than experiment in founding the classical theories of elasticity and vibration.

Motion of a Rigid Cylinder Due to a Plane Elastic Wave
View Description Hide DescriptionThe motion of a rigid cylinder resulting from a normally incident, monochromatic, plane, elastic wave of either P (longitudinal) or S (transverse) type is calculated. Numerical results are presented in the form of curves.

Electromagnetic Reflection from Sound Waves
View Description Hide DescriptionThe reflection of electromagnetic waves normally incident on the wavefronts of a semi‐infinite standing sound wave in a liquid is discussed theoretically. Since the reflecting planes of maximum sound pressure disappear periodically, the reflected electromagnetic signal is modulated with the acoustic frequency. The modulated reflected electromagnetic wave arises (1) from the microscopic movement of the liquid surface, and (2) from the direct analog of Bragg reflection in optics. The second effect is most pronounced when the wavelength of the electromagnetic radiation in the liquid is twice the acoustic wavelength.