Volume 39, Issue 5A, May 1966

Fifty Years of Physical Ultrasonics
View Description Hide DescriptionThe experimental investigations that first showed excess of sound absorption in gases above the classical value are described, and the theoretical ideas that lead to their explanation by relaxation processes are discussed. A survey is then given of later progress, which is closely connected with the rapid development of electronics, and of the parallel refinement of the theory. The work in liquids started somewhat later. The theoretical situation is more complex, but, for that very reason, ultrasonic measurements in liquids give information about problems absent in gases. The consideration of viscous liquids led to a connection with the behavior in glasses, in accordance with Simon's theory. In metals, the starting point, the methods, and the important frequency range for loss measurements were originally different; but here, too, the investigations and theoretical viewpoints have been multiplied and diversified.

Low‐Frequency Scattering by Soft Spheroids
View Description Hide DescriptionThe exact series solution for the scattering of a plane wave by a soft spheroid is used to obtain explicit long‐wavelength approximations. The farfield scattering amplitude is given to the sixth power of the frequency and the near field is given to the second power. The results are valid for prolate and oblate spheroids and arbitrary angles of incidence and observation.

Propagation Modes of Infrasonic Waves in an Isothermal Atmosphere with Constant Winds
View Description Hide DescriptionA dispersion relation for low‐frequency disturbances in an isothermal atmosphere with constant horizontal winds is derived. It relates the three components of the wave‐propagation vector k to the angular frequency ω and depends on the sound speed, the wind velocityv, and the acceleration of gravity g. The relation is obtainable from that for propagation in an isothermal atmosphere without winds if ω is replaced by ω−k⋅v. The dispersion relation is studied with reference to the problem of the propagation of waves from a stationary source of limited spatial extent viewed by a stationary observer. The topology of the propagation surface in k space is examined. Propagation modes are defined as corresponding to disjoint portions of the surface in k space for fixed ω. The criteria for a given mode existing for given wind speed and frequency are derived and the group velocity of each type of mode is studied. The theory predicts the existence of two wind modes that, at sufficiently high frequencies, have group velocities nearly identical to the wind velocity. Phase velocities of the wind modes also tend to equal the wind velocity. In the latter portion of the paper, the trajectories of fluid particles are studied for each type of wave‐propagation mode. It is shown that, in terms of particle motions, the wind modes are physically indistinguishable from the gravity mode predicted for an isothermal atmosphere at rest when viewed by an observer moving with the wind.

Impedance of Tapered Structures
View Description Hide DescriptionThe exact solution for the impedance of a manifold of differing but uniform transmission lines is derived. The number of uniform structures contained in the manifold is arbitrary and can be increased without bound. The exact solution to the manifold is used to obtain the impedance of a continuously tapered structure having a characteristic impedance and a velocity of propagation that varies along the length of the structure. This solution to the continuously tapered structure can be made as accurate as desired. An approximation to the continuous solution is derived that is valid provided the maximum value of the product of the internal reflection coefficient and the wavelength is much less than unity. The application at this approximate solution to the synthesis of tapered structures is discussed.

Frequency Equations for Wave Propagation in an Initially Stressed Circular Cylinder
View Description Hide DescriptionThis paper describes the derivation of frequency equations for the propagation of small sinusoidal waves in an infinitely long isotropic elastic cylinder that has been initially stressed.

Large‐Amplitude Linear Vibrations of Tensioned Strings
View Description Hide DescriptionThe transverse motion of a tensioned string driven parametrically by a moving end support is examined both analytically and experimentally. The conditions required to linearize the equations of motion for vibrations over a large‐amplitude range at constant frequency are developed and shown to be physically realizable.

Particle Waves and Audiofrequency Modes in Crystals
View Description Hide DescriptionStarting with the idea that wave mechanics should be useful in dealing with mechanical properties of solids, a connection between particle waves and deformation in crystals is developed. The connection is one in which Planck's constanth plays a prominent part. According to the view described, nonelastic deformation in crystals arises through the propagation of internally generated particle momentum waves with the de Broglie wavelength λ = h/mv_{i} . Here, m and v_{i} are the mass and velocity, respectively, of certain, initially field‐free atoms that exist because of lattice defects in the crystal. The particle waves in question are not the probability waves of contemporary, orthodox quantum theory which satisfy the Schrödinger equation. Instead, real‐property waves governed by a new differential equation are proposed. Solutions to this equation for both finite and infinite lattices lead to frequency‐wave vector conditions from which a number of interesting results follow. These include the occurrence of characteristic frequencies or modes associated with nonelastic deformation, and, in particular, the existence of discrete audiofrequency modes whose frequencies depend on Planck's constant, atomic mass, and lattice segment length. The particle‐wave view thus leads directly to predictions of nonelastic audiofrequency resonances in vibration experiments and to expectations of acoustic emission during unidirectional plastic deformation. Applications of these same ideas to other aspects of mechanical behavior are also described briefly.

Observations of Nonelastic Audiofrequency Resonances
View Description Hide DescriptionAdditional experimental evidence and analysis are presented that tend to confirm the fundamental nature of previously reported nonelastic audiofrequency modes or resonances in solids. The evidence cited includes some results recently advanced by others to demonstrate that the resonances arise from contact and/or apparatus effects, but these results really confirm the resonances as material properties. The particle‐wave view of deformation is also strongly supported by these same, supposedly adverse, experimental results.

Vibration of Cantilever Beams to which Dynamic Absorbers are Attached
View Description Hide DescriptionThe simultaneous application of two dynamic absorbers to an undamped cantilever beam is discussed theoretically. The dynamic absorbers possess viscous damping. They are tuned and damped in the so‐called optimum manner for which it is possible to suppress the resonances of the beam in a uniform and symmetrical fashion. The beam is exalted by a sinusoidally varying force situated either at its free end or at its midpoint. It is to these locations that the dynamic absorbers are attached. The absorbers are tuned to suppress the first and second beam resonances, the optimum values of absorber tuning and damping depending upon the location of the absorbers and upon the beam resonance that is of concern. In addition to the rôle of the absorbers in suppressing the first and second beam resonances, excitation of the third resonance is essentially avoided when the driving force is situated at the midpoint of the beam because a nodal point of the third mode occurs very near to the beam center.

Steady‐State Responses of One‐Dimensional Periodic Flexural Systems
View Description Hide DescriptionExpressions are derived that describe the steady‐state behavior of infinitely long beams with uniformly spaced attached impedances and that permit damping and fluid loading to be taken into account readily. The case where the attached impedances produce only lateral forces is treated on the basis of classical beam‐flexure theory. Relations governing the segment‐to‐segment propagation constant and the impedance the system presents to a force acting at an impedance attachment point are derived; the response to forces acting at all impedance attachment points, with a constant phase difference between adjacent forces, is also deduced. Additional results, applicable only in the region outside the near fields of the impedance attachment points, in cases where the interval between attached impedances encompasses many flexural wavelengths, are formulated in terms of the reflection and transmission coefficients that are effective at the impedance attachment points, and thus apply for impedances of any degree of complexity. A corresponding expression for the propagation constant is obtained, and a method (which is suitable also for numerical analysis of a wide variety of complex one‐dimensional systems) is developed for determining the steady‐state oscillations resulting from a given wave or waves injected at a given location.

Transient Response of Thin Elastic Shells
View Description Hide DescriptionA solution for the transient response of a thin elastic shell that rests on a viscoelastic foundation is found by means of the mode‐acceleration method. For a uniform load, this solution is compared with a similar solution obtained by means of the mode displacement method. A numerical example for a hemispherical shell illustrates that the mode acceleration method converges slightly more rapidly that the mode‐displacement method during the time of application of the transient pulse.

Surface‐Wave Propagation in a Continuously Stratified Medium
View Description Hide DescriptionThe problem of long range propagation in a continuously stratified medium is considered for those cases where the stratification is such that a region of slow sound velocity is found to be embedded in a region of relatively faster sound velocity. It is then possible to explain the guiding mechanism of the medium in terms of surface‐wave theory. The technique employed utilizes an equivalent integral‐equation representation for the differential equations describing the boundary‐valve problem, and yields information concerning the dispersive character of the medium. As a means of illustrating the mechanics of this technique and demonstrating its application, dispersion curves are obtained for the particular case of propagation in the sofar sound channel.

Long‐Range Deep‐Sea Attenuation Measurement
View Description Hide DescriptionA series of standard U. S. Navy explosive charges was dropped by an aircraft en route from Bermuda to Brazil, and recordings were made at various hydrophone locations of the missile impact locating system in the Atlantic. Data from the Bermuda station have yielded attenuation coefficients between 10 and 480 cps for deep‐sea propagation over a total pathlength of 2600 miles. The results are compared with the compilation made by Thorp [J. Acoust. Soc. Am. 38, 648–654 (1965)]. The data suggest a low‐frequency relaxation process as one of a number of possible attenuation processes of sound transmission in the deep sea.

Reduction of Aircraft Noise Measured in Several School, Motel, and Residential Rooms
View Description Hide DescriptionField noise reduction measurements in 21 school, motel, and residential rooms during flyovers of jet and propeller aircraft are described. The measured noise reduction for most rooms was found to lie within or near the range of moderate noise‐reduction values observed in previous measurements of houses and wood‐frame air‐base buildings. Sizeable differences in room noise reduction values were observed during successive aircraft flyovers. For jet‐aircraft flyovers, the root‐mean‐square value of the standard deviations for noise‐reduction measurements in school and motel rooms was 2.7 PNdB. For the four residential rooms studied, a root mean‐square value for the standard deviations of 3.4 PNdB was observed.

Amplitude of Békésy Tracings with Different Attenuation Rates
View Description Hide DescriptionAmplitude measurements of threshold fixed‐frequency Békésy tracings were made for interrupted and continuous tones on normal and pathological ears. Comparison of four attenuation rates (1, 2, 4, and 8 dB/sec) on the same subjects indicates that bottoms of spikes were at similar sound‐pressure levels (SPL) foe different attenuation rates both for interrupted and continuous tones, while the tops and midpoint of spikes were at significantly different levels as attenuation rate varied. Standard audiometry thresholds related best with the SPL of bottoms of spikes of pulsed‐tone tracings in both normal and pathological ears. Doubling the attenuation rate changes amplitude in the ratio of about 1 to 1.62 and increases pen reversals per unit time in the ratio of approximately 1 to 1.23. This is true for both interrupted‐ and continuous‐tone tracings for all frequencies in both normal and pathological ears. Separation between interrupted‐ and continuous‐tone tracings in pathological ears is not significantly different for various attenuation rates when measured between bottoms of spikes for different attenuation rates.

Pitch Discrimination of Jittered Pulse Trains
View Description Hide DescriptionListeners are presented with pulse‐train stimulus pairs and asked to judge whether they can hear a difference between them. The interval between pulses is a random variable, identically and independently distributed for each stimulus of a pair. Two distributions are observed: one, nominally Gaussian, and the other, nominally the distribution of the amplitude of a sinusoidal wave whose phase is uniformly distributed. The principal experimental parameters are the mean interval between pulses and root‐mean‐square deviation or jitter about this interval. The stimuli of each pair are identical in other respects—pulse shape (50‐μsec pulse width), loudness (30 or 35 dB sensation level)—but differ in polarity pattern. Two pattern combinations are observed. For the range of mean pulse intervals investigated, 5–15 msec, the stimuli of each pair are generally discriminable when unjittered. However, the results indicate that, when jittered in amounts greater than 1 or 1.5 msec, the stimuli may be rendered nondiscriminable. This critical amount of jitter coincides with a flattening of the power‐density spectra of the stimuli for frequencies greater than 250 or 200 cps. On the basis of this result and the results of other investigations, it is hypothesized that the correlates of discrimination for unjittered or lightly jittered stimuli are distinct neural volley patterns associated with basilar‐membrane activity in the 300‐ to 1000‐cps region.

Coupled Thickness Shear and Flexure Displacements in Rectangular AT Quartz Plates
View Description Hide DescriptionThe length variation of the thickness‐shear and thickness‐flexure modes in rectangular ATquartz plates are computed from Mindlin's first order theory, which assumes particular thickness variation. These curves are compared with the mode shapes determined experimentally by measuring the x‐ray intensity diffracted from vibrating quartz plates. The diffracted x‐ray intensity is proportional to the curvature, a combination of strain‐gradient terms of the Bragg planes, which may be approximated from the first‐order theory. The approximation for the curvature is quite good for modes that are essentially thickness shear. When the mode has a large flexure component, the approximation used to determine the curvature of the Bragg planes is not as accurate.

Wall Vibrations in Flue Organ Pipes and Their Effect on Tone
View Description Hide DescriptionThe question of the effect of wall vibrations on the tone of an organ flue pipe is examined theoretically and experimentally. The effect of nonrigid walls is calculated and it is shown that, if they do not affect the pipe frequency, they do not radiate appreciably. For pipes as ordinarily constructed of circular or nearly circular cross section, the lack of rigidity of the walls will have negligible effect. The wall vibrations actually occurring in sounding organ pipes were investigated experimentally and found to be owing to the vibrating air stream from the flue impinging on the lip. By artificially vibrating pipes to the same acceleration levels as when blown, it was found that the sound radiated from the vibrating walls is negligible. By surrounding pipes with a jacket and filling the space between with water, it was determined that the wall vibrations do not affect the internal standing wave in the pipe. Measurements of pipes in other organs confirmed the laboratory findings. It is concluded that the steady tones of organ pipes are not affected by wall vibrations.

Choice of Reference Conditions for Speech Preference Tests
View Description Hide DescriptionPreference tests used in the evaluation of speech‐communication systems typically employ as reference conditions different levels of one type of distortion, produced by a single reference system. A new preference test has been developed to explore the possible advantages of using several reference systems that represent fundamentally different types of distortions. The new test was experimentally compared with the more conventional test, and it was found that the preference judgments obtained with the new test exhibited a significantly smaller variance among the listeners. This finding suggests that, by using several reference systems that represent an appropriate variety of distortions, preference tests can be constructed that are more efficient than those developed to date.

Statistics of F2 Adjacent to Consonants and Prediction of F2 Onsets
View Description Hide DescriptionThe purpose was to evaluate ways of predicting the onset frequency of the second vowelformant (F2) following consonant constrictions. Spectrograms of 604 constrictions were measured to obtain the frequency and slope of F2 offset just prior to each constriction, the duration of the constriction, and the frequency of F2 onset after the constriction. Three types of F2 onset prediction were applied to each constriction: (1) holding the F2 offset frequency, (2) linear extrapolation of F2 offset slope, and (3) exponential extrapolation of the offset slope. Statistical analyses of these data indicated that linear extrapolation gave poor results, that holding predictions were superior to predicting merely the modal onset, and that exponential extrapolations were better than holding offsets under certain conditions of offset slope and frequency region. Articulatory place and complexity of consonant constriction were found to be related to prediction error.