Volume 43, Issue 5, May 1968

Underwater Sound and Naval Acoustical Research and Applications before 1939
View Description Hide DescriptionThis report describes some of the highlights of underwater sound and other naval acoustical technology in the United States during the period of World War I to World War II. A number of accomplishments in subaqueous acoustics of the Naval Research Laboratory are given, emphasizing sonar equipment research and development. Acoustic studies in air and ocean environments carried out at NRL are also described; and a general glimpse of the research climate in the early decades of NRL is portrayed.

Propagation of One‐Dimensional Waves from a Source in Random Motion
View Description Hide DescriptionThis paper is concerned with the transient problem of waves in an infinite one‐dimensional medium owing to a monochromatic source whose position X(t) is a stochastic function of time. Asymptotic results for the farfield are given for the general class of stationary source motions and for the case in which X(t) is a Wiener process, corresponding to Brownian motion.

Wave Propagation in Anisotropic Bars of Rectangular Cross Section. Part I. Longitudinal Wave Propagation
View Description Hide DescriptionAn approximate solution is obtained for the problem of steady‐state longitudinal‐wave propagation in anisotropic bars of infinite length and rectangular cross section by employing the variational method of Ritz. The first three dispersion curves are presented for orthotropic, tetragonal, hexagonal, cubic, and isotropic systems.

Acoustic Radiation from a Finite Line Source with N‐Wave Excitation
View Description Hide DescriptionA shock wave with an N‐shaped pressure profile is propagated in the equatorial plane of a weak spark in air. In the present work, the directional dependence of the acoustic waveform is examined for 0.5‐ and 1.0‐cm sparks having discharge energies between 0.01 and 0.1 J. The transient signals are detected with a wide‐band capacitormicrophone that has a rise time of less than 1 μsec. As the spark axis is approached, an interval with no acoustic disturbance appears near the center of the waveform. The angular dependence of both the shock amplitude and the length of this central interval is found to be in qualitative agreement with the results of a linear analysis in which it is assumed that each point along the spark acts as a source of N waves.

Analysis of Elastically Coupled Piezoelectric Resonators
View Description Hide DescriptionThis paper presents an analysis of an elastically coupled piezoelectric resonator system consisting of a linear array of two or more counter electrode pairs placed on the major surfaces of a quartz crystal plate. Each pair of counter electrodes establishes resonator having a transverse thickness mode of motion. The equations describing this system are derived and applied to an array of ncoupled resonators and specific numerical computations are made for the cases where n is equal to 2, 3, and 6. These results are plotted and show the dependence of the effective interresonator coupling on the dimensions of the electrode configuration.

Growth of Acceleration Waves in Isotropic Elastic Materials
View Description Hide DescriptionThe growth of acceleration waves propagating in an isotropic elastic material is examined. The underlying assumption made is that the material is at rest in its reference configuration. First, we establish that only longitudinal or transverse acceleration waves may propagate, and the wave speeds are determined. Then, we derive the differential equation governing the growth of the amplitude of longitudinal acceleration waves and obtain explicit solutions for plane, cylindrically or spherically expanding waves. These results indicate that the amplitude of acceleration waves may either decay to zero in infinite time or become infinite (shock formation) in finite time; the radius effect on the amplitudes of cylindrical or spherical acceleration waves are not of the form or 1/r, as predicted by lineary theory. On the other hand, the behavior of transverse waves is similar to that obtained by linear theory.

Resonant Properties of Piezoelectric Ceramic Rectangular Parallelepipeds
View Description Hide DescriptionThis paper is concerned with the resonant properties of free, piezoelectricceramic rectangular parallelepipeds, such as cubes. By means of the calculus of variations, the electroelasticdifferential equations are transformed into an approximate matrix characteristic value problem. Solution of this problem yields the resonant frequencies, the particle displacement patterns at resonance, and the equivalent circuit parameters such as the motional capacitances. Structures of the present type possess eight distinct symmetry families of modes; however, only one of these is excitable piezoelectrically with two opposite faces completely electroded. The resonant frequencies of the first 50 modes of this family are presented graphically versus Poisson's ratio for the special case of an isotropic cube. The frequency and dynamic capacitance of the first 30 modes of the same family are given for a piezoelectricceramic square cylinder as the thickness‐to‐width ratio is varied from zero (thin square plate case) to unity (cube case). This result demonstrates the fact that the so‐called thickness mode of a thin plate is actually a composite of many high contour‐extensional overtones. Numerous modal displacement patterns are sketched for the square cylinder and cube special cases. Lastly, experimental results are reported that correspond reasonably well with the theory: Agreement is on the order of 3% for resonant frequency values and 20% for other quantities.

Wave Propagation in a Sandwich Ring
View Description Hide DescriptionThe propagation of small‐amplitude free harmonic waves in an elastic sandwich ring is studied by using a Timoshenko‐type theory, which takes into account the effects of radial shear deformation, rotatory inertia, and extension of the neutral axis. The form of the equations of motion is the same for both homogeneous and sandwich rings, but the range of values for the parameters involved in the latter case can lead to qualitative changes in the wave propagation characteristics of the system. It is shown that the ratio of the ring's extensional stiffness to its shear stiffness has an important influence on the frequencies and group velocities of sandwich rings. When this ratio becomes large, two of the three modes of wave propagation become less dispersive. Numerical examples are presented and discussed.

Vibration Analysis of Stiffened Cylinders including Inter‐Ring Motion
View Description Hide DescriptionAn analytic method is presented for the determination of the vibrational characteristics of ring‐stiffened cylindrical shells. The stiffening rings, which are assumed to be uniform and evenly spaced, are treated as discrete members, and the inter‐ring shell motions are fully and exactly accounted for within the linear shell theory used in the analysis. The flexural, extensional, and torsional rigidities of the rings are retained in the analysis as well as all in‐plane inertia terms. Numerical comparison made with the results from existing energy methods and orthotropic model approach. It is found that for high circumferential wavenumbers, the inter‐ring displacements may become very pronounced.

Deep‐Sea Noise Due to Surface Motion
View Description Hide DescriptionA physical model is proposed for the deep‐sea ambient noise. Ambient noise is hypothesized to be caused by the high‐frequency caipllary patches that are randomly distributed over the ocean surface. The random surface‐roughness spectrum implied by the ambient‐noise measurements and that implied by the hypothesis are discussed. The results are found self‐consistent and comparable to those of other investigators. They also agree with the idea of convolution radiation (proposed by) Longuet‐Higgins, Marsh, and Kuo. The analysis strongly indicates simple relationship among the physical parameters controlling ambient noise,noise frequency f, noise direction θ, and the sea state (implied by λ_{ w }). The relationship is given by 2π/λ_{ w } = 2πf sinθ/c _{ w }, where λ_{ w } is energy containing gravity wavelength, c _{ w } is acoustic velocity in the water, and θ is radiation direction with respect to the normal of the mean sea level. When one physical parameter was arbitrarily held constant, the other two physical parameters varied consistently with actual measurements.

Creeping‐Wave Analysis of Acoustic Scattering by Elastic Cylindrical Shells
View Description Hide DescriptionThe Sommerfeld‐Watson transformation is applied to the normal‐mode solution of a plane sound wave being scattered by an infinite elastic cylindrical shell immersed in a fluid and containing another fluid. The resulting residue series is generated by poles that are the complex zeroes of a 6×6 determinant. These zeroes are found numerically by an extension of the Newton‐Raphson method for complex functions. As in our previous work on sound scattering by a solid cylinder, it is found that besides the infinity of the well‐known rigid zeroes, there exists a set of additional zeroes that gives rise to generalized Rayleigh and Stoneley waves. The behavior of these zeroes has been studied as function of the wavenumber and also of the shell thickness. The bistatic cross section was evaluated numerically and compared with experiments.

Fluctuation in Horizontal Acoustic Propagation over Short Depth Increments
View Description Hide DescriptionUnderwater acoustic‐propagation measurements have been made off Key West, Fla., for the past 3 yr. Two or three deep‐submergence vehicles were allowed to sink freely and simultaneously through the water to depths as great as 5000 ft while transponding acoustically with each other. Pulses at frequencies of 10, 20, and 40 kHz and horizontal ranges of 1700 to 8000 yd were used in the experiment. Because direct acoustic signals showed amplitude fluctuations of approximately 15 dB for depth changes of 15 20 ft, a method of rapid pulsing was installed. This allowed the emission of discrete signals 0.25 sec apart over a period of 5 sec periodically during an operation. Amplitude fluctuations for depths changes of only a few inches could be measured. Pulse‐to‐pulse amplitude differences of up to 15 dB were found for depth changes of as little as 10 in. These fluctuations are discussed in terms of transmission loss and are compared to the losses suffered for the larger depth changes and for those predicted by ray theory on the basis of the measured sound‐velocity structure of the water. It is concluded that refraction conditions can account for the fluctuation.

Spoiler‐Generated Flow Noise. I. The Experiment
View Description Hide DescriptionWe discuss the growing importance of forms of aerodynamic noise other than classical jet noise in the modern gas‐turbine engine. An experiment is described in which, on a model scale, the sound‐generating capabilities of a flow spoiler within the environment of a pipe have been studied. A selection of results is presented. These show some of the principal findings of the study and the appearance of a correlation scheme for spoiler noise based on the total pressure drop across the spoiler.

Spurious Pressure Fluctuations in Wind Tunnels
View Description Hide DescriptionWall pressure spectra measured in wind tunnels usually exhibit a pronounced rise at low frequencies, in conflict with theoretical predictions and with those experiments carried out without the constraint imposed by the wind tunnel. Some wind tunnel experiments are described to show that typically the spurious disturbances arise in the first diffuser and travel upstream as acoustic waves. Removal of the diffuser produces a spectrum falling at low frequencies.

Source Size as a Theoretical Limitation on the Determination of Wave Vectors by Detector Arrays
View Description Hide DescriptionAn important class of infrasonicwaves in the atmosphere and seismic waves in the earth's crust are generated by ocean waves in marine storms. The determination of wave vectors from such large sources by detector arrays is limited by the systematic errors introduced by the large sources, as well as by the resolving power and ambiguities associated with any given array configuration. The apparent phase lag and coherency between two detectors, each receiving signals from the multitude of mutually incoherent oscillators comprising a large source, is discussed as a function of source size and source‐detector configuration. It is found that the apparent phase lags between two detectors may deviate from the phase lag of a ray from the source center. As a result, the apparent phase lags among the detectors in an array may lead to an apparent wave vector discrepant with the wave vector from the source center. Empirical results are presented to confirm the validity of this approach in the case of microbarom generation by ocean waves.

Practical Problems of Partition Design
View Description Hide DescriptionIt is proposed that partitions should be classified according to the insulation that is required. Up to 35 dB, a single‐wall construction may be used; but, for an average transmission loss of 40 dB or more, it is more efficient to use a double‐leaf type of construction. A given insulation may then be obtained either with light leaves and a large cavity or with heavy leaves and a small cavity. The difficulties associated with both single and double walls are discussed, and it is shown that, with care, the detrimental effects of both wall and cavity resonances may be either eliminated or very much reduced. The classical theory for double‐wall transmission is found to be inadequate; but an empirical design formula gives good agreement with measured average values.

Practice Effects in the Absolute Judgment of Pitch
View Description Hide DescriptionThree experiments are reported in which the relation between practice and the absolute judgment of pitch was examined. Experiment 1 showed that students with training in music could judge pitch more accurately than students with little or no music training. In Expts. 2 and 3, listeners were given systematic training that stressed the identification of a single reference standard −A_{4}, 440 Hz. Following such training, listeners showed improved recognition of A_{4} (Expt. 2) and improved recognition of a series of 10 tones (Expt. 3). Training on the reference standard A_{4} was more effective in improving the performance of music students than was training in which the listener was required to name each tone and was then told the correct response (regular feedback).

Some Properties of Longitudinal Shear Waves: A Study by Computer Simulation
View Description Hide DescriptionShearing between the basilar membrane and tectorial membrane is known to contribute towards mechanical processing of the auditory signals. The amplitude of the longitudinal shear wave has been given by von Békésy to be proportional to the vertical amplitudes of the basilar membrane and the first space derivative of the momentary position of the traveling wave along the basilar membrane. Traveling waves were generated on a digital computer using a modified form of Flanagan's mathematical model. Shear waves were obtained from these by taking the first instantaneous space derivatives. Envelopes for the longitudinal shear vibrations are compared to those of the traveling waves. These comparisons show that: (1) The maxima of the shear wave envelopes are slightly closer to the helicotrema. (2) The shear waves are much more localized along the basilar membrane. (3) Localization is much more pronounced at low frequencies than the equivalent entities of the traveling wave. Comparisons made between the resonance curves of traveling‐wave vibrations and shear‐wave vibrations show considerable sharpening of the shear‐wave envelopes towards the low frequencies. The effect of middle ear transmission on the resonance curves is shown.

Further Results on Binaural Unmasking and the EC Model. II. Noise Bandwidth and Interaural Phase
View Description Hide DescriptionData are presented on binaural unmasking of tones masked by noise as a function of the interaural phases of the tone and noise and the bandwidth of the noise. It is found that (1) for a tone of 250 Hz, the binaural unmasking increases by 10 dB as the bandwidth is reduced from 250 Hz to 4.2 Hz; (2) the functional form of the dependence on interaural phase is independent of bandwidth; (3) reducing the bandwidth increases the amount of unmasking at all frequencies; (4) previous versions of the EC model are inadequate for describing the results; and (5) the data can be described by assuming that the error factor k in the EC model depends on the bandwidth W and interaural phase θ_{ n } of the noise according to a relation of the form .

Some Effects of Tonal Interactions as Seen in the Cochlear Microphonic
View Description Hide DescriptionThe microphonic response recorded from the round window of anesthetized cats with implantedelectrodes was studied using stimuli consisting of two pure tones. Filtered or unfiltered responses were displayed oscillographically with sweeps phase locked to the low‐frequency stimulus component. This permitted study of the amplitude modulation of the higher‐frequency, components by the low‐frequency stimulus. Complex modulation effects were found in all animals studied. Modulation envelopes could be either simple, with one maximum and one minimum per cycle of the low‐frequency stimulus; or double, with two maxima and two minima per cycle. Simple modulation tended to be produced at lower SPL's of the low‐frequency stimulus than double modulation. The phase of the modulation envelope relative to the low‐frequency signal varied in some cases with the frequency and intensity of each stimulus component. For suitable frequency pairs, the phase angle of the low‐frequency component of the cochlear response could be reduced by raising the SPL of the higher‐frequency stimulus. When both stimuli were raised to high SPL's, the modulation pattern could shift by 180°. Results are qualitatively discussed in terms of a heuristic model involving stimulation of nonlinear “unit” generators by traveling waves.