Volume 40, Issue 2, August 1966

Segmentation of Speech Sounds
View Description Hide DescriptionA program for segmentation of an acoustical continuum of speechsounds into discrete parts suitable for further analyses is described. The speechwave is read into the computer using an A‐D converter. Analysis is performed directly on the acoustic waveform, using an IBM‐7090. The pattern‐recognition techniques used to segment the acoustic waveform into sustained and transitional parts are discussed. Some results obtained by the computer program are given.

Ultrasonic and Hypersonic Studies of Vibrational Relaxation in Benzene
View Description Hide DescriptionUltrasonic absorption measurements have been made in benzene over the frequency range from 7 to 570 Mc/sec at 6° and 25° C. Velocity measurements at both ultrasonic and hypersonic frequencies also were made in the temperature range 6°–60°C. The observed relaxationeffects may be interpreted in terms of double relaxation of the vibrational specific heat.Analysis of the absorption data indicates that the vibrational specific heat associated with all but the lowest vibrational mode relaxes in the ultrasonic range, with the measuredrelaxation frequency varying from 510 Mc/sec at 6°C to 560 Mc/sec at 25°C. Correlation of the ultrasonic and hypersonic data also indicates a second relaxation frequency (associated with the lowest vibrational mode) of the order of 10 Gc/sec.

Attenuation and Dispersion of Sound by Particulate‐Relaxation Processes
View Description Hide DescriptionThe temperature and velocity of a particle suspended in an acoustic field are subject to fluctuations that may lag behind those of the surrounding fluid. A theory for acoustic attenuation and dispersion in an aerosol based on these particulate‐relaxation processes is given. The close relationship between particulate relaxation and relaxation mechanisms due to lagging molecular or atomic internal degrees of freedom is displayed. The particulate‐relaxation theory predicts attenuation and dispersion by small, heavy particles, in close agreement with existing, more‐detailed theories, for values of ωτ_{d}, (ω is the circular acoustic frequency, τ_{d} is the dynamic relaxation time of the particle) smaller than and including order unity. Comparison with existing experimental data of attenuation and dispersion [J. W. Zink and L. P. Delsasso, J. Acoust. Soc. Am. 30, 765–771 (1958)] shows good agreement. However, the existence of a maximum attenuation per wavelength, when ωτ_{d} ≈ 1, that is predicted by the theory is not tested by the above experiments, which were conducted with ωτ_{d} > 1. Similarly, the maximum dispersion that occurs at the low‐frequency limit was not tested in the previous experiments.

Long‐Wavelength Scattering by Hard Spheroids
View Description Hide DescriptionThe exact series solution for the scattering of a plane wave by hard spheroids is used to obtain explicit long‐wavelength approximations in powers of k = 2π/λ, where λ is the wavelength. The far field scattering amplitude is given to the sixth power of k and the nearfield is given to the second power. The results are valid for prolate and oblate spheroids and arbitrary angles of incidence and observation.

Exact Solutions for the Propagation of Two Simple Acoustic Transients in Waveguides with Perfectly Reflecting Walls
View Description Hide DescriptionThe response of a fluid‐filled waveguide with perfectly rigid or pressure‐release boundaries and uniform cross section to acoustic transients propagated down the axis of the guide is studied. Exact solutions are obtained for step‐function and gated sine‐wave excitations of the source. The particle velocity resulting from the latter input can be written as the sum of the familiar steady‐state solution and a transient signal composed of two Lommel functions. An approximate expression is obtained that allows quantitative estimation of the behavior of the first portion of the transient as a function of the dimensionless parameter zλ/a ^{2}, where a is the radius of the waveguide,z is the distance that the transient has traveled, and λ is the free‐field wavelength associated with the carrier frequency of the gated sine wave. Some experimental confirmations of the predicted waveforms are presented. The relevence of these propagation effects on the accuracy of velocimeters is discussed.

Vibration of a Spherical Shell in an Acoustic Medium
View Description Hide DescriptionThe basic equations for axisymmetric, nontorsional vibration of a spherical shell in an acoustic medium are obtained by the use of Lagrange's equations. Dynamic displacements and the pressure in the fluid were obtained for the case of forced motion of the shell under a harmonic, concentrated force.

Acoustic Radiation from a Wobbling Piston
View Description Hide DescriptionThe sound field of a circular piston in an infinite rigid plane baffle is calculated when the motion of the piston consists of the conventional uniform velocity normal to the plane of the piston plus a wobbling motion about a diameter of the circle: as an axis. There is a net resultant moment owing to the wobble; this moment is proportional to an integral of the square of the farfield pattern function over real and imaginary angles. A wobble impedance is defined as the moment divided by the angular velocity of the wobble. The real part of the wobble impedance is obtained from the integral of the square of the farfield pressure over real angles, and the imaginary part is obtained from the real part by the use of the Kramers‐Kronig, or dispersion relations. Numerical results for the wobble impedance are presented. It is shown that for small pistons a merely wobbling piston is less efficient as a generator of sound than the customary uniform‐velocity piston.

Transmission of Sound through a Circular Membrane in a Plane Wall
View Description Hide DescriptionThe acoustic system studied is that of a plane, rigid wall having a circular window in it, across which is stretched a membrane under tension, in contact with an acoustic medium on both sides. A plane wave of frequency ω/2π is directed at one side of the wall plus membrane, at an angle of incidence θ. The integral equations relating the motion of the membrane and the pressure difference across the membrane are obtained. Fairly accurate solutions to these two equations are then obtained by a variational procedure. Values of the functions involved are plotted and tabulated. Formulas are derived for the total power transmitted through the membrane and for the distribution in angle of the transmitted wave; typical plots are given of the results. These are discussed to demonstrate the contribution of the membrane resonances and anti‐resonances to the transmitted wave. It is known that an unbounded membrane is transparent to an incident plane wave when the wavenumber of the transverse wave in the membrane is equal to the component of the incident wavenumber parallel to the membrane. The solution for the transmission through a membrane of finite size, obtained in this paper, shows how the resonances and antiresonances, typical of the finite membrane, radically modify the transparency effect.

Method of Calculation of Frequencies of Partially Fixed Beams Carrying Masses
View Description Hide DescriptionIn this paper, a convenient method is presented for obtaining a closed‐form (not series) solution for solving the problem of free vibrations of a partially fixed beam, with unequal end fixities, and carrying an arbitrary number of concentrated masses in an arbitrary way. The method utilizes finite Fourier sine transforms. By this method, the simplified frequency equations to a general case and two special cases are given. The eigenfrequencies of a partially fixed beam (equal end fixities) with a mass in the middle and at quarter‐span are evaluated numerically; and the results of the former are compared with those of an earlier publication, where the classical method is utilized.

Flexural Vibrations of a Circular Ring when Transverse Shear and Rotary Inertia are Considered
View Description Hide DescriptionThe partial‐differential equations derived by Reissner, Uflyand, and Mindlin governing the motions of plates are solved for a plate bounded by circular contours and radial lines. Two cases have to be considered. They are: Case I: a plate bounded by circular contours and radial lines (r = r _{1}, r = r _{2}, r _{2} > r _{1}; θ = θ_{1}, θ = θ_{2}); Case II: a plate bounded by two concentric circles (r = r _{1}, r = r _{2}, r _{2} > r _{1} … circular ring). The solution for each partial‐differential equation is an infinite series of product solutions. Case I cannot be solved by product solutions because of the impossibility of satisfying boundary conditions along the radial lines θ = θ_{1} and θ = θ_{2}. Case II is solved for each of the eight different boundary conditions entering into this theory for each eigenvaluem = 0, 1, 2, … Hence, after the elimination of the arbritrary constants for m = 0, 1, 2, …, the frequency equation for each problem is obtained by solving a determinant of sixth order equated to zero. A comparison between the classical theory and the present theory, which includes coupling between flexural and shear motions, for the case of the clamped circular ring is included.

Torsional‐Wave Propagation from a Rigid Sphere Semiembedded in an Elastic Half‐Space
View Description Hide DescriptionTwo problems of torsional‐wave propagation from a rigid sphere semiembedded in an elastic half‐space are solved in closed form. The first problem treated is the motion of the elastic solid when the angle of twist of the sphere about a vertical line is a given function of time. The second problem is the motion of the sphere and elastic solid when the sphere is subjected to a time‐dependent torque about the vertical axis.

Coupled Vibratory‐System Analysis, Using the Dual Formulation
View Description Hide DescriptionPrinciples by means of which an arbitrary vibrational system may be cut into subsystems and described by coupled modal equations are exposed and illustrated with an elementary example. The symmetry of the equations attainable when both the usual geometric description and the dual or force space representation are used is shown. The difficulties in use and interpretation of the coupled equations when the coupling is not weak are discussed.

Free Vibrations of a Slender Bar with Nonuniform Characteristics
View Description Hide DescriptionThe free vibrations of a slender bar with characteristics slightly different from those of a uniform one are discussed. A simple approximate solution to this problem is presented. Results from experiments conducted with a bar of variable cross section in free‐free flexural vibrations indicate that the theory adequately predicts resonant frequencies and nodal locations.

Use of Instantaneous Axes for Determining Small Oscillations
View Description Hide DescriptionA theorem is presented and proved that establishes points about which the equation of angular momentum simplifies for small (linear) oscillations of a rigid body. Thus, a fourth criterion in addition to the well‐known three conditions of classical mechanics is established. An illustrative example is given.

Propagation of Harmonic Flexural Waves in an Infinite Elastic Rod of Elliptical Cross Section
View Description Hide DescriptionThe potential equations of motion of a linear elastic solid are employed to study the propagation of a class of harmonic flexural waves in an infinite rod of elliptical cross section with a stressfree surface. Using the separation solutions to these equations, a frequency equation is obtained in the form of an infinite determinant set equal to zero, the elements of which involve Mathieu functions and their derivatives. When the eccentricity goes to zero, this determinant can be written in diagonal form, the terms of which, when set equal to zero, describe the propagation of flexural and circumferential modes of odd order in a circular rod.

Reverberation under Arctic Sea‐Ice
View Description Hide DescriptionReverberation from explosive sounds detonated beneath uniform young summer sea‐ice were recorded in September 1964 in the Arctic Archipelago. Backscattering strengths were obtained for three octave bands between 1.28 and 10.24 kcps, and for grazing angles between 10° and 70°. The reverberation measured is significantly lower than that measured under well‐rotted polar pack ice in September 1963 [J. R. Brown, J. Acoust. Soc. Am. 36, 601–603 (L) (1964)], and a great deal lower than the results obtained by Milne in April [A. R. Milne, J. Acoust. Soc. Am. 36, 1551–1556 (1964)], under pressure‐packed one‐year ice. A strong dependence of under icebackscattering on surface roughness is thus indicated.

Reverberation from Deep Scattering Layers in the Western North Atlantic
View Description Hide DescriptionReverberation from deep scattering layers was measured at 37 sites in the western North Atlantic. Resonant scatterers, presumably the swimbladders of bathypelagic fish, were responsible for the bulk of the observed reverberation. Three scattering layers, each populated with a characteristic size of scatterer, were found to persist over distances of several hundred kilometers. During the day, these layers were at depths between 300 and 900 m. A migration towards the sea surface of scatterers from the shallowest layer at sunset appeared to be responsible for most of the low frequency reverberation observed at night. The majority of the scatterers from the deepest of the layers did not experience a daily migration in depth. Two of the layers studied showed pronounced decreases in depth with increasing latitude. No seasonal variations in scattering strengths were observed.

Analysis of Electroacoustical Transducers by Differential Immittance Techniques
View Description Hide DescriptionTechniques are in use for the measurement and recording of the impedance and admittance loci of electroacoustical transducers at various levels of input power. The resulting data are used for determining properties such as piezoelectric coefficients, mechanical Q, resonant frequency, potential efficiency, etc. An extension of these techniques has now been developed to provide direct measurements and graphic recordings of the difference between two admittances or impedances. This approach may be used to separate the motional impedance or admittance circle from the complete locus without the need for lengthy arithmetical manipulations and also to read the minor component of impedance or admittance with greater accuracy than has heretofore been possible in direct‐reading systems. This approach has also been applied to the measurement of the dielectric loss and capacitance of piezoelectrics under high voltage and to the separation of time‐variant components of impedance from time‐invariant components.

Acoustic Scattering from Fluid Spheres
View Description Hide DescriptionThe problem of scattering of sound from fluid spheres is investigated for the case where the acoustical properties of the sphere and surrounding medium are very similar. This similiarity allows Bessel functions with arguments related to acoustic properties inside the sphere to be expressed in series expansions of Bessel functions, with arguments related to the acoustic properties outside the sphere. Using only the fiirst‐order terms in the expansions results in simpler solutions than the exact case for plane‐wave conditions in the backscattered direction. The amplitudes and time dependences for backscattered acoustic pulses can then be calculated to first order in the differences in density and bulk modulus of the two media. Higher order terms are very complicated, and a convenient way of determining the time dependences of these terms has yet to be obtained.

Measured Structure of Harmonics Self‐Generated in an Acoustic Beam
View Description Hide DescriptionThe acoustic beam from a circular plane piston 1.01 cm in radius, driven sinusoidally to finite amplitudes in water, at 2.58 Mc/sec, has been mapped with two quite different small probes about 2 mm in diameter. Equivalent acoustic pressures at the source ranged from 0.2 to 6.0 atm. The fundamental component and the self‐generated second and third harmonics were filtered separately, and beam patterns were photographed on a CRO screen. Fine structure down to the size of the probes was recorded. Reliability was demonstrated both by agreement of the two different probes and by measurements on theoretically known patterns at very low amplitude; maxima and minima were, respectively, lowered and raised in the records, but approximate analytical corrections are available. Rough estimates (±30%) of sensitivity showed that both probes were substantially linear and stable. The second‐harmonic component of the beam was found to be more nearly cylindrically collimated than was the fundamental. Fine structure in second and third harmonics was rather less complex than in the fundamental, and different in detail, yet the higher harmonics were not much nearer than the fundamental to being collimated plane waves.