Index of content:
Volume 61, Issue 4, April 1977

Adjointness properties for differential systems with eigenvalue‐dependent boundary conditions, with application to flow‐duct acoustics
View Description Hide DescriptionWhen the boundary conditions at the two endpoints of a second‐order differential system depend explicitly upon the eigenvalues such that the system becomes non‐self‐adjoint, a generalized condition of orthogonality which includes endpoint terms can be developed. The generalized orthogonality condition is used to determine modal coefficients for the expansion of arbitrary functions in series of eigenfunctions. The method is applied to the particular case of acoustic wave propagation in a rectangular duct with a uniform mean‐flow profile and walls with finite acoustic impedance. The ability of the eigenfunction expansion to converge to a plane‐wave acoustic pressure profile is demonstrated under a variety of flow, frequency, and wall‐impedance conditions.

Interpretation of radiation fields in terms of sub‐beams
View Description Hide DescriptionTwo frequently employed measures of a statistical radiation field, i.e., the mutual coherence function and the acoustic‐intensity angular spectral density, are considered as they apply to deterministic beamed signals. Mathematical formulations, in the form of differential equations, that govern the propagation of these measures had previously been presented [J. J. Mcloy and M. J. Beran, J. Acoust. Soc. Am. 59, 1142–1149 (1976)]. Here, we show that solutions of these formulations suggest an interpretation of a radiation field in terms of sub‐beams. These sub‐beams are the natural extensions of the ray tubes of the geometric theory. In the Appendix we consider the relationships between the acoustic‐intensity angular spectral density and other more commonly encountered measures of a radition field.

Reciprocity relations for scattering of plane, elastic waves
View Description Hide DescriptionThe reciprocity relations that apply to the scattering of plane, elastic waves that are incident upon an obstacle of finite extent are investigated. In these relations, the particle‐displacement radiation characteristics of the scatteredwaves occur. The elastic medium outside the obstacle is assumed to be homogeneous, isotropic, and perfectly elastic. Hence, two kinds of acoustic waves can propagate in it, viz., irrotational, compressional or Pwaves and solenoidal, shear or Swaves; each of these two waves has its own radiation characteristic. It is shown that the far‐zone scatteredwave due to an incident wave propagating in the direction ? and observed in the direction −? is related to the far‐zone scatteredwave due to an incident wave propagating in the direction ? and observed in the direction −?. This reciprocity property is next applied to two incident Pwaves, two incident Swaves, and an incident Pwave and an incident Swave. The resulting reciprocity relations hold under the assumption that the scattering obstacle is linear and reciprocal in its elastic behavior.

Electric and acoustic waves in continuously coupled distributed coupling transducers
View Description Hide DescriptionA distributed coupling transducer consists of an electric and an acoustic transmission line continuously and reversibly coupled to each other. The operation of this device is described by four coupled first‐order differential equations. The solution to these equations is obtained in closed form for both infinite and finite transmission‐line systems. The example of a side‐plated piezoceramic bar is considered in setting up the equations. A comparison between the complete theory and an approximation based on the infinite transmission line is given. Some aspects of the design of a high‐efficiency, broadband electroacoustic transducer with a relatively constant resistive electrical driving‐point impedance are presented.

Amplitude and phase fluctuation periods for long‐range propagation in the ocean
View Description Hide DescriptionIt is commonly observed in long‐range propagation that the phase fluctuation period is longer than that of the amplitude. A phase‐random multipath model, used previously to explain amplitude statistics [I. Dyer, J. Acoust. Soc. Am. 48, 337–345 (1970)], is now applied to the joint problem of amplitude and phase. The ratio of phase period to amplitude period is found to be proportional to a Rayleigh probability density, with a peak value of about three. This result is supported by data acquired by the Woods Hole Oceanographic Institution and analyzed by us, for a 300‐km propagation path extending approximately northeast from Eleuthera.

Low‐frequency acoustic fluctuations and internal gravity waves in the ocean
View Description Hide DescriptionAcoustic phase and amplitude fluctuations measured during two experiments, one near Eleuthera Island and one near Bermuda, are presented and interpreted in terms of the interaction of sound with internal gravity waves. Data were collected with a variety of sensors including drifting ship‐suspended hydrophones, sonobuoys (free‐floating acoustic receivers equipped with a UHF transmitter for data communication), and moored hydrophones. The phase data were corrected for hydrophone motion by means of a bottom‐moored Doppler navigation system. Oceanographic data are presented and compared with the acoustic data; these data comparisons show that internal waves are responsible for much of the acoustic fluctuations. Phase spectra obtained with moored hydrophones show a rapid spectral decay at frequencies above the highest osberved Brunt–Vaisala frequency as predicted by internal‐wave–acoustic models. Spectra obtained with drifting hydrophones are compared with a recently proposed random, multipath model based on interaction of sound with internal waves. Spectra obtained for drifting hydrophones at a depth of 1500 m agree with the multipath‐model prediction. Spectra from phones at shallower depths exhibit an order of magnitude more fluctuation energy than is predicted. Slowly drifting sonobuoys at a depth of 300 m produce spectra with a complex frequency dependence that can not be predicted by the random multipath model.

Temporal light modulation in thick‐screen diffraction by ultrasound beam plus amplitude grating
View Description Hide DescriptionTemporal modulation of light obtained by a diffraction device consisting of an ultrasonic beam and an optical grating has been theoretically described under the hypotheses of diffractioneffects not superposed (thick‐screen treatment). In comparison with any thin‐screen theory considering spatially superposed effects, the present thick‐screen treatment is in better agreement with the experimental results.

Surface waves of an elastic medium in the presence of an inviscid flow field
View Description Hide DescriptionThe stability of an elastic layer being excited by a flow field is examined. The dynamics of the elastic layer is assumed to be governed by the basic elasticityequations. On the lower surface the layer is assumed to be fixed to a rigid surface. On the upper surface, a potential flow field is assumed to provide the exciting force. A solution to the linearized set of elasticity and fluid‐mechanics equation is obtained. When all of the boundary conditions are satisfied, a compatibility equation is obtained. Complex and real eigenvalues of this equation for different Poisson’s ratio, Young’s modulus, and flow velocity have been obtained. In the limit as the fluid density goes to zero the classical Rayleigh surface waves are recovered.

Reflection and refraction of transient waves in fluid‐filled porous media
View Description Hide DescriptionIn this study, reflection and refraction of transient waves in a nonhomogeneous fluid‐filled porous body is investigated. The body involves a layer of one porous material perfectly bonded to a half‐ space of another porous material. Transient waves are generated at the top surface of the layer by a time‐dependent applied pressure. For a variety of material properties chosen for the layer and half‐space, the time variations of various physical quantities are found at two stations: one in the layer, the other in the half‐space. A study of numerical results, obtained by the method of characteristics, indicates that the rigidity of the half‐space relative to that of layer strongly affects the reflection and refraction characteristics of transient waves with regard to sign while the relative permeability of the half‐space has an influence on their dispersive characteristics.

Approximate formulas for natural frequencies of rectangular plates with linearly varying thickness
View Description Hide DescriptionA characteristic equation is derived analytically for a rectangular plate with thickness varying linearly in one direction by using the trigonometric series. Boundary conditions of the plate are simply supported along two opposite sides, free along one side and simply supported or free along the remaining side. By using the results computed numerically from the characteristic equation, approximate formulas are derived for estimating accurately the fundamental natural frequency of the plate.

Resilient mounting of machinery on platelike and modified platelike substructures
View Description Hide DescriptionThe problem of isolating machinery vibration from platelike substructures is analyzed. Simply supported, internally damped, square, rectangular, and circular plates are considered, as are rectangular plates with rigid cross members that divide the plates into separate quadrants. The machinery is supported either by eight or by four antivibration mounts located symmetrically about the plate centers. The attachment of dynamic vibration absorbers or lumped masses to the plates at each mount location is shown to be effective in reducing the force transmitted to the plate boundaries. The dynamic absorbers are tuned to suppress transmissibility at the fundamental resonance of the plate of concern, whereas the lumped masses become effective at frequencies above this resonance where their impedance predominates that of the plate. Utilization of the circular and quadrant plates greatly reduces the number of plate resonances that contribute to the force transmitted to the plate boundaries. Further, when machinery is supported by four antivibration mounts on square and rectangular plates, the number of resonances that are excited can also be reduced significantly if the mount locations are chosen judiciously. However, the use of other mount locations can yield a large number of pronounced resonances in excess of those excited when the machinery is supported by various arrangements of eight antivibration mounts—for which transmissibility does not appear to change greatly with the choice of mount location.

Wave propagation along a sapphire rod
View Description Hide DescriptionWe consider the propagation of elastic waves along a circular rod composed of sapphire or of another material with the same elastic symmetry. We obtain an analytical description of the modes by making an infinite‐series perturbation expansion about an expression which describes waves along a transversely isotropic rod.

Torsional vibrations of a sapphire rod: A numerical description
View Description Hide DescriptionA numerical description of the lowest‐order torsional mode of vibration of a c‐axis sapphire rod is obtained from two approximate theories. One theory involves an infinite series perturbation expansion about an expression which describes modes along a thransversly isottropic rod. The other theory involves a low‐frequency asymptotic expansion for the lowest‐order torsional mode of spphire. At frequencies for despersive; its phase and group velocities are obtained. The mode can be visualized as consisting of towq waves which travel down the rod π/2 rad out of phase. In one wave, each cross section rotates rigidly ints cross section undergoes a transverse distortion. Both the warping and the transverse distortion have a threefold symmetry about the rod axis.

Sound transmission through periodically framed parallel plates
View Description Hide DescriptionThe problem of transmission of a plane sound wave through two infinite parallel plates connected by identical periodically spaced frames is solved. Fluid loading within and without the cavity space is taken into account. Numerical results are presented corresponding to a standard double‐walled partition. The strengths of the two parallel transmission paths, i.e., the structural path through the studs and the airborne path through the cavity space, are compared.

Sonar velocity resolution with a linear‐period‐modulated pulse
View Description Hide DescriptionFor linear‐period‐modulated (LPM) signals, the p h a s e of the echo from a moving‐point target contains information about range rate. When an LPM signal is transmitted, a Doppler‐insensitive sonar processor is obtained by following a matched filter with an envelope detector. Velocity information can be extracted from the same echo, however, if the receiver is sensitive to phase. A receiver that envelope detects matched‐filter responses and also estimates the phase of an echo can therefore be b o t hDoppler tolerant and Doppler resolvent. If LPM is used, only two matched filters are needed to implement a sequence of M velocity hypotheses, rather than a bank of M different filters. LPM is thus an excellent signal format not only for Doppler‐invariant range estimation and initial detection, but also for fine velocity resolution with minimum receiver complexity. The existence of velocity‐induced phase transformations in LPM signals also leads to a new synthetic aperture sonar technique.

Masking‐period patterns produced by very‐low‐frequency maskers and their possible relation to basilar‐membrane displacement
View Description Hide DescriptionBy using masking‐period patterns (MPP), produced by sinusoidal as well as impulsive maskers with very‐low‐frequency components, it could be demonstrated for man that the basilar membrane seems to move in phase for low sinusoids and preserves the waveform for nonsinusoids with low‐frequency spectrum within the two basal turns of the cochlea. The shape of a MPP is strongly correlated to the second derivative of the time function of the sound pressure at the eardrum for frequencies below 40 Hz, but to the first derivative for frequencies above 40 Hz. This is presumably due to the form of the cross section of the cochlea and the size of the helicotrema in man. Data of many MPP are shown and discussed together with patterns given in former papers on a qualitative and a quantitative level, leading to the following proposal: the higher peak in MPP belongs to a kind of suppression which would correspond to the displacement of the basilar membrane towards scala tympani, while the lower peak in MPP belongs to the excitation which would correspond to the displacement of the basilar membrane towards scala vestibuli.

Minimum differences of level and frequency for perceptual fission of tone sequences ABAB
View Description Hide DescriptionStream segregation or fission of the fast alternating tonesequence ABAB is known to occur if there is a sufficient frequency difference between the tones A and B. In this paper it will be shown that level difference instead of frequency difference can be sufficient to enable the occurrence of fission. The smallest level difference between A and B, ΔL?3 dB (2.5–10 tones per sec; tone duration 40 msec). At rates faster than 12 tones per sec a new perceptive phenomenon was observed: the roll effect. It is characterized by the weak tones being heard at double the tempo. The relation with the continuity effect is investigated using alternating sequences with both level and frequency difference between the tones as stimuli.

Correlations of duration for nonadjacent segments in speech: Aspects of grammatical coding
View Description Hide DescriptionTwo speakers read versions of the following sentence: D i c k w i l l t a k e t h e j e e p x C l a r k w i l l t a k e t h e t r u c k, in which x was one of the conjunctions a n d, b u t, s i n c e, or i f. Each sentence was read 40 times. Product‐moment correlations were computed for segment durations in all word pairs involving D i c k, t a k e _{1}, j e e p, C l a r k, t a k e _{2}, and t r u c k. Statistically significant correlations were obtained for both speakers, particularly for the sentence containing the coordinate conjunction a n d. The results showed positive correlations for words having the same grammatical relation (subjects, verbs, direct objects) lying on opposite sides of the major clause boundary. Positive correlations were also obtained for the two contrastively stressed words in the second clause (C l a r k, t r u c k). Negative correlations were obtained primarily between noncontrastive words within each clause. The results suggest that a speaker’s grammatical code plays a role in regulating speech timing and that this influence is not restricted to the domain of a single clause.

Video‐scanning system for measurement of lip and jaw motion
View Description Hide DescriptionAn instrument for measuring labial and mandibular positions during speech is described. A modified video system is used to measure the positions of small reflecting glass beads attached at selected points on the face and to a thin wire anchored on a mandibular tooth. The system allows continuous data collection from up to 16 reflector points at a sampling rate of 100 Hz. Reflector movements with instantaneous velocities up to 45 cm/sec can be determined with a 0.3‐mm resolution. Techniques for data acquisition and analysis and display are described.

Computer‐aided signal handling for speech research
View Description Hide DescriptionOf the total time and effort expended on an experiment in speech research, a significant fraction is usually spent on signal‐handling tasks such as collecting and inspecting speech tokens, and making test tapes. Such tasks can be done more quickly, easily, precisely, and reliably with the aid of an interactive signal‐handling program implemented on a laboratory computer. This paper describes how Editor, a versatile yet easy‐to‐use signal‐handling program at Bell Laboratories, is used to cope with a variety of signal‐handling tasks in speech research. The paper seeks to create an awareness of the scope and power of computer‐aided signal handling by describing Editor as a working model. The description emphasizes concepts relevant to the design and implementation of any system for handling signals with the aid of computers.