Volume 45, Issue 5, May 1969

Computers in Acoustics: Symbiosis of an Old Science and a New Tool
View Description Hide DescriptionThis paper reviews the impact of digital computers on acoustics research since their introduction about a decade ago. The influential rôle that computers have attained in acoustics has resulted from their imaginative use as research tools for analysis, control of experiments,modeling, and simulation—rather than from straightforward calculating applications. Illustrative examples discussed in this paper include modeling of the human speech‐production process and the mechanical and neural aspects of hearing, speech analysis and synthesis, automatic speech and speaker recognition, generation of musical sounds and psychoacoustic test stimuli, study of the perceptual correlates of acoustic stimuli, multidimensional scaling, simulation of ray propagation in the deep ocean and in reverberant enclosures, acoustic measurements in concert halls, digital modeling of auditorium designs. Monte Carlo simulation of wave propagation in multimode transmission media, and acoustic image reconstruction of unknown objects by “inverse diffraction” on the computer.

Large‐Amplitude Damped Free Vibration of a Stretched String
View Description Hide DescriptionThe equations of motion of a vibrating string are derive, and it is shown that a coupling exists between the longitudinal and transverse modes of vibration. Free transverse vibration of small order, under sinusoidal initial conditions, is analyzed. Under these conditions, the equations are separable. The time‐dependent parts of the equations are solved by the method of variable amplitude and phase. It is seen that, when the vibration is nonplanar, part of the energy oscillates between the mutually perpendicular transverse components with a frequency proportional to the nonlinearity parameter α. The path of any point on the string is shown to be an ellipse with slowly rotating and shrinking axes.

Response of Uniform Beams to Homogeneous, Random Pressure Fields
View Description Hide DescriptionA study of the expression for the response power spectral density of linear systems to random pressures shows that the response problem essentially reduces to evaluating the joint acceptance of the system with the pressure field. A novel method using a coordinate transformation is presented. This method enables one to determine very simply the joint acceptance of a beam that has arbitrary end constraints with a pressure field that has a spatial‐pressure correlation function that is easily described mathematically. The joint acceptance of a simply supported beam with a reverberant acoustic field as a function of mode number and nondimensionalized frequency parameter (beam length/acoustic wavelength) has been computed for the first 16 modes. An engineering approximation for the joint acceptance of a simply supported flat plate with a reverberant acoustic field is obtained from the beam results. The method is also used to determine very simply beam and flat‐plate joint acceptance with a turbulent‐boundary‐layer pressure field and with an acoustic plane wave.

Effect of Edge Vibrations on the Propagation of a Strain Transient
View Description Hide DescriptionThe Mindlin‐McNiven equations are used to study the response of a linearly elastic semi‐infinite rod to a time‐varying pressure suddenly applied to its otherwise free end. The solution is presented as the sum of two parts. The first part is the response that is obtained if the end to which the pressure is applied is restrained from any radial motion. The second part represents the difference in response that arises due to a relaxation of this radial constraint. A numerical investigation of the latter term in the Fourier transform domain discloses two poles, symmetrically placed with respect to zero frequency, which are close to but immediately below the real frequency axis. These poles are the source of the edge‐resonance phenomenon for steady vibrations that has been reported by McNiven and are also the source of the long tail noted in the experiments of Oliver. The form of the correction term in the real time domain is obtained by the method of steepest descent for times in the vicinity of that at which a saddle point comes closest to colliding with each of these poles in the complex frequency plane.

Analytical and Experimental Studies of Multiple‐Unit Impact Dampers
View Description Hide DescriptionThe exact solution for the symmetric two impacts/particle/cycle motion of an n‐unit impact damper attached to a sinusoidally excited primary system is derived analytically, and its asymptotically stable regions are determined. Simulated motion on a digital computer and experimental studies with a mechanical model are presented, and they show good agreement with theoretical results. It is found that properly designed multiple‐unit impact dampers are more efficient than equivalent single‐unit impact dampers in regard to vibration reduction and noise level of operating units.

Cross Correlation in Structural Systems: Dispersion and Nondispersion Waves
View Description Hide DescriptionThe use of cross correlation as a tool for analyzing propagation of energy in structural systems is investigated. Each energy‐transmission path will have a characteristic delay time, and examination of the cross‐correlation function of input and response can guide in the determination of the most significant path or paths. Difficulties occur in distributed systems or when the propagation is by a dispersive mechanism. The principles of correlation analysis are examined for both dispersive and nondispersive systems. Experimental evidence is presented that supports the theory and concepts developed. On the basis of these preliminary results, it appears that the technique holds promise and bears further investigation.

Analysis of an Integral Equation Arising from the Investigation of Vertical Directivity of Sea Noise
View Description Hide DescriptionAn integral equation relates the single frequency vertical distribution of ambient oceannoise to the measured array output when the noise power at the array arises from the superposition of uncorrelated plane waves. This integral equation has an infinite number of solutions. However, from the physical viewpoint, there is one solution, referred to as the “principal solution,” which is the most plausible representation of the true noise field. The “principal solution,” is precisely defined, and then classical Hilbert spacetheory is used to determine this solution from a finite number of array measurements. The number of measurements required depends only on the interelement spacings of the array. In selecting this finite number of steering angles to make the array measurements, any choice that yields independent samples for a certain finite sequence of trigometric functions is sufficient. Not surprisingly, these measurements contain all the information available in the observed distribution, the array output, and an explicit expression is given for the observed distribution. Special array configurations are exhibited for which the “principal solution” is a partial sum in the Fourier expansion of the true noise field.

Pulsed Circumferential Waves on Aluminum Cylinders in Water
View Description Hide DescriptionThree types of waves that contribute to the total acoustic diffracted field of an aluminum cylinder in water are isolated by generating each wave to the exclusion of the other two. The “Franz‐type” or “creeping” wave is generated separately on the outside of aluminum cylinders with ka values ranging from 54 to 1008. The circumferential‐wave speed is found to be 1% less than that of the free waterborne wave, in agreement with the theory for a rigid cylinder. The attenuation of these waves on aluminum cylinders is significantly less than that predicted by the theory for the rigid cylinder. Another circumferential wave, with approximately a 30° incidence and emergence angle, is found to propagate on the inside of the curved boundary. This wave has an attenuation ranging between 0.10 and 0.18 Np/rad and has a speed of 2.5 times that of the free waterborne wave. This is classified as a “Rayleigh type” wave. A third wave is observed that is similar to the wave generated at 30° incidence but has a 15° incidence and emergence angle. The attenuation is between 0.08 and 0.14 Np/rad and has a speed of 6.5 times that of the free waterborne wave. Experimental measurements of differential‐scattering cross section are compared with those calculated by means of the creeping‐wave formulation.

Acoustic Propagation in a Channel with Range‐Dependent Sound Speed
View Description Hide DescriptionRay geometry, travel time, and spreading loss are studied in a horizontal channel in which sound speed depends on range. Formulas valid for a general sound‐speed function are developed, and then specialized to the class of linear functions. Rays reaching a fixed receiving point are then isolated and studied. Properties of corresponding arrivals at a fixed receiving point are compared for the cases of a range gradient channel and a constant sound speed channel. Differences in initial inclination angle, travel time, and spreading loss are found and bounds on these differences are obtained. For a CW source, the total field at a receiving point is then determined. It is demonstrated that the introduction of even a weak range gradient causes major changes in the amplitude and phase, including the occurrence of interference nulls accompanied by a sharp offset in phase. Finally, approximate formulas are developed for the phase shift of the total field, caused by a constant range gradient, relative to the phase in isospeed channels.

Stability of a Plane Shock Wave in Free Space and in the Presence of Rigid or Interfacial Boundaries
View Description Hide DescriptionThe attenuation of small perturbations in the shape of a plane shock wave is studied for three distinct cases — (A): when a rigid boundary (wall) parallel to the plane of the unperturbed shock is present; (B): when a perturbed interface between two different media exists in the wake of the shock; (C): when there is no boundary (free space). The solution is obtained by extension of a method due to Zaidel. It is shown that for weak shock waves the attenuation becomes very weakly dependent on the nature of the boundary. Numerical results are obtained for shock waves with initially sinusoidal perturbations and initially Gaussian perturbations. For initially sinusoidal perturbations, Case (A) shows the slowest damping (highest peak‐to‐peak ampli‐after some time) whereas Case (B) exhibits the most rapid damping. On the other hand, an initially Gaussian perturbation shows the slowest damping (magnitude of maximum disturbance) for Case (B) and the fastest damping for Case (A). Furthermore, the Gaussian perturbation damps monatonically with time whereas the sinusoidal perturbation damps approximately in the manner of a zero‐order Bessel function — i.e., in an oscillating fashion.

Theory of Holographic Interferometry
View Description Hide DescriptionA simple theory of three forms of holographic interferometry “time‐average,” multiple‐exposure, and “real‐time” (live) interferometry is presented, based on a new development in holographic “image synthesis” (complex amplitude addition and subtraction), introduced in 1965 by D. Gabor and G. W. Stroke et al. They demonstrated the remarkable property of holography: Interference can occur between two or more light beams that are not superimposed either in time or in space, if the holographic intensities corresponding to the beams are obtained with the aid of a coherent reference‐background beam of the same spatial shape and if these intensities are successively added in the same hologram. Following the independent discovery of holographic interferometry, in 1965, by J. M. Burch; by R. L. Powell and K. A. Stetson; and by L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, among others, it was found that two or more successive photographic additions of the hologram intensities (corresponding to two or more sequential positions or shapes of a given object) would thus indeed permit one to “synthesize,” in the form of an interferogram, the complex sum of the spatial‐electric‐field vectors, corresponding to each object‐point position, as if the different object‐point positions had all existed simultaneously rather than sequentially, as they do during the hologram recording (for instance in the case of multiple holographic‐image recording of a vibrating object). The rigorous equations we present, notably in vector form, for the general cases of practical interest bear out the equations previously derived by a number of authors, for some special cases, frequently in heuristic form.

Perception of Pitch in a White‐Noise Mask
View Description Hide DescriptionThree mel scales, derived from fractionation data, and representing three differential noise conditions are obtained. It is found upon comparison that the presently found no‐noise function differs in no essential manner from the generally accepted mel scale advanced by Stevens (1940). However, upon the introduction of a wide‐band masker, the shape of the mel function becomes more positively accelerated. In general, when holding the intensity of the masker constant, this acceleration is inversely related to the sensation level of the experimental tones above masked threshold, and is not frequency dependent. Although this relationship is not dependent upon frequency per se, the magnitude of pitch shift increases with frequency.

Monaural Loudness‐Intensity Relationships for a 1000‐Hz Tone
View Description Hide DescriptionThis investigation was designed to obtain the monaural loudness function for a 1000‐Hz tone. Ten trained observers with normal hearing were utilized. The method used was the numerical magnitude balance procedure. This investigation indicates that the results obtained by the numerical magnitude balance procedure are repeatable if the observers do not have previous knowledge of the decibel scale, and if they are properly trained. This is indicated by the good agreement of the results of this study with the findings of previous studies. The results of this study showed a loudness exponent of 0.54 based on data averaged by geometric means and 0.51 based on data averaged by medians.

Dichotic Summation of Loudness
View Description Hide DescriptionThe over‐all loudness of a pair of equally loud tones presented dichotically, a different frequency to each ear, is independent of the frequency separation between the two tones. This rule applies over the whole range of frequency separations tested, from 0 Hz to several thousand hertz; hence, dichotic tone pairs are just as loud as a binaural pair (same frequency to each ear). Both binaural and dichotic pairs, however, are generally less than twice as loud as a component presented by itself. The over‐all loudness is invariant even though at narrow frequency separations the components of a dichotic pair interfere with each other so that each component is softer when heard in the presence of the other than when heard by itself. At wide separations, where two distinct auditory images are reported, the loudness of a component is the same whether presented with or without the contralateral tone.

Effects of Pure‐Tone Masking on Low‐Pass‐ and High‐Pass‐Filtered Noise
View Description Hide DescriptionThreshold measurements were obtained for low‐pass‐ and high‐pass‐filtered noises in the presence of pure tones in normal subjects. High‐pass‐filtered noise with cutoff frequencies at 2400 Hz and above yielded masking peaks near the cutoff frequencies. When noise was filtered with cutoff frequencies at 1200 Hz and below, pure tones of 800 and 1000 Hz had the greatest masking effect. For low‐pass‐filtered noise, as the bandwidth increased, masking peaks moved from low frequency to high. The masking effect was indistinguishable from that of white noise when filtered noise was cutoff at frequencies of 2400 Hz and above. These results suggest that there is a definite mechanical resonant frequency effect on noise when the width of filtered noise exceeds a critical value. Masking effects are discussed in relationship to mechanical resonant frequency and the interaction of difference and summation tones.

On the Utilization of Ferrofluids for Transducer Applications
View Description Hide DescriptionAn assessment of the suitability of ferrofluids for acoustic transducer and receiver applications has led to the following conclusions: First, the magnetostrictive mode of operation is not efficient enough to offer an alternative to conventional solid materials in use. Second, the piston motion of the ferrofluid induced by an applied field gradient does provide a real alternative to conventional magnetostrictive transducers. For an applied static field of 4000 Oe and a field gradient of 1000 Oe/cm, it is possible to achieve an overall efficiency that is greater than that for the ferromagnetic solids. Third, ferrofluids appear to provide a desirable alternative for pressure‐sensing applications in severe environments (e.g., detonations) where piezoelectric and pyroelectricmaterials suffer fatigue and failure. Fourth, ferrofluids offer the prospect of obtaining broadband frequency response when radiating or receiving in liquid media.

On the Motor Control of Coarticulation in CVC Monosyllables
View Description Hide DescriptionThis study was an attempt to account for the motor control of speech production by a model in which discrete phoneme commands are modified according to phonological context by three motor system mechanisms. The model was evaluated by consideration of high‐speed cinelluorograms, and electromyograms from nine articulatory locations, recorded while one subject produced 36 consonant‐vowel consonant monosyllables. The syllables were formed by every possible combination of initial and final consonants /b/, /d/, and /g/, and the syllable nuclei /i/, /u/, /æ/, and /ɔ/. In every possible case, some aspect of the motor control of a later syllable component was influenced by the identity of the previous one. Except in a few cases, some aspect of the motor control of an earlier syllable component was influenced by the identity of the following one. These latter influences were of greater magnitude and complexity, and more reflected in movement, in the initial consonant than in the vowel. Some of the context effects on phonemes could be accounted for by the three motor system mechanisms but a number could not. The results suggested that syllabic factors are influential in the “premotor” command structure of speech, and, in particular, that the CV form is a relatively cohesive component of CVC syllables.

Acoustic Pulse Distortion in Thermally Relaxing Liquids
View Description Hide DescriptionPulse propagation in a thermally relaxing liquid is studied theoretically. First, Whitham's theory of wave propagation in systems governed by more than one velocity is utilized to obtain qualitative information. Second, Laplace transform solutions are obtained for particle velocity and pressure for rectangular and Gaussian pulses as well as semi‐infinite sine wave. Detailed numerical calculations are included.

Elastic Wave Propagations and Acoustical Birefringence in Stressed Crystals
View Description Hide DescriptionThe elastic wave propagations in deformed crystals with any symmetry are investigated theoretically. The rotationless acoustical tensor, which specifies the propagation condition, consists of the tensor based on the natural unstressed state and the perturbation term being proportional to the stress. The perturbation theory is applied to nondegenerate and degenerate cases with respect to the quasitransverse wavevelocities. The perturbed wavevelocities and the polarization directions are formulated by the stress suppressed on the crystals, and then the general formulas for the acoustical birefringence depending on the second‐ and third‐order elastic constants are reduced. The difference of the quasitransverse wavevelocities is expressed by the sum of two terms: the difference of these in unstressed crystals due to the intrinsic anisotropy and the perturbation term due to the stress. In the cases of the cubic system and of the isotropic material, the explicit relations are calculated. For the isotropic material, the so‐called stress‐acoustical law holds.

Experimental Detection of Evanescent Ultrasonic Waves by Bragg Diffraction of Light
View Description Hide DescriptionThe presence of evanescent ultrasonicwavesdiffracted from an acoustic grating has been detected using Bragg diffraction of laser light. The diffraction of light by these evanescent waves (whose concept stems originally from theoretical arguments) confirms their physical existence. The grating used was designed to diffract the sound into two kinds of wave components: (1) a single propagating wave component moving directly away from the grating; and (2) a pair of oppositely directed evanescent‐wave components traveling along the back surface of the grating and forming a standing evanescent wave with exponential decay perpendicular to the grating. Such evanescent waves have shorter wavelengths than propagating waves and hence are inherently capable of better resolution if used for imaging. With the proper orientation of the laser beam with respect to the grating, theory predicts that the above wave components will produce diffracted spots of light symmetrically placed about a central axis. The spots due to the evanescent‐wave components are found on an axis perpendicular to that of the spots due to the propagating‐wave component, and the evanescent‐wave spots are further away from the center. Detection and measurement of the positions and the relative intensities of the spots gives information about the wavelengths of the components and about the rate of exponential decay of the evanescent wave.