Volume 31, Issue 9, September 1959
Index of content:
31(1959); http://dx.doi.org/10.1121/1.1907845View Description Hide Description
Techniques are presented for approximating integral solutions to some problems in theoretical seismology. The approximations obtained are the first terms of asymptotic series in powers of t−t 0, where t is the time and t 0 is an arrival time. The approximations are obtained by evaluating the integral form of the Laplace transform of the time solution by the saddle point method or a variation of it. To the resulting expression is applied a Tauberian limit theorem from which is obtained the time solution. Two examples are given which illustrate some of the specific techniques for the use of the method.
31(1959); http://dx.doi.org/10.1121/1.1907846View Description Hide Description
The exact solution to the problem of the scattering of compressional elastic waves from a line source by a rigid, infinitely dense cylinder imbedded in an isotropic, homogeneous, perfectly elastic medium is obtained in integral form. The integrals are evaluated asymptotically obtain the motions on the wave fronts. In the illuminated zone the saddle point method of integration yields the geometrical optics approximation to the reflected field. In the shadow zone the diffracted field is obtained by evaluating the integrals by the method of Dougall and Watson. In the case of an incident P wave the observed events in the illuminated zone are (1) direct P, (2) reflected P, and (3) reflected S. In the shadow zone the observed events are (1) diffracted P and (2) diffracted S. Both diffracted wave fronts travel around the cylinder with the velocity of P waves.
31(1959); http://dx.doi.org/10.1121/1.1907847View Description Hide Description
The directional and frequency diffusion of a plane monochromatic sound wave in statistically homogeneous, isotropic, and stationary turbulence is analyzedtheoretically. The treatment is based on the diffusion equation for the energy density of sound waves, using the scattering cross section derived by Kraichnan for the type of turbulence assumed here.
A form for the frequency wave number spectrum of the turbulence is adopted which contains some pertinent parameters of the flow and is adapted to ease of calculation. It is expected that the assumed spectrum is unrealistic at larger wave numbers. A new approach to the evaluation of the characteristic period of the flow is suggested. This spectrum is then related to the scattering cross section.
Finally, a diffusion equation is derived as a small‐angle scattering approximation to the rigorous transport equation. The rate of spread of the incident wave in frequency and direction is calculated as well as the power spectrum and autocorrelation functions for the wave.
31(1959); http://dx.doi.org/10.1121/1.1907848View Description Hide Description
Flexural wave propagation and damping in multilayer plates is treated theoretically with use of impedance techniques. These techniques yield equivalent electrical circuits whose behavior is determined either by standard circuit analyses or by analog electrical measurements. The properties of two types of multilayer damping treatments are investigated detail. The first type is a two‐plate system enclosing a viscous liquid. The viscous liquid may also contain pressure‐release partitions. The second type investigated consists of a layer of an air‐filled porous material placed between a plate to be damped and an array of masses. Flexural wave measurements carried out on these multiple plates are shown to be in good agreement with calculations. It is shown that the viscous liquid layer and the porous layer may have high loss tangents in particular frequency ranges. With the use of the impedance techniques, a comparison made between the damping treatments studied and two other damping treatments that have Been investigated earlier by Oberst and Kerwin.
31(1959); http://dx.doi.org/10.1121/1.1907849View Description Hide Description
The effect of noise regeneration by fluid flow on the performance of noise‐attenuating structures is examined with special attention to muffler design. The insertion loss of a single element, as well as a continuous distribution of attenuating and noise‐regenerating elements, is studied. For example, in a duct with an attenuation constant β per unit length and a regeneration r per unit length, the upper limit of the insertion loss is 10 log (2Eβ/r), where E is the source strength. It should be noted that the insertion loss of a noise‐regenerating attenuator depends on the sound level to be reduced.
An analysis of experimental data on jet noise indicates that the power spectrum of a circular jet depends on frequency, f, and Mach number, M, approximately as f 2 M 5 at low frequencies, as f −2.5 M 9.5 at high frequencies, and as M 7 at the peak frequency. In terms of the corresponding jet spectrum, for which an empirical analytical expression is given, the maximum attainable insertion loss of a jet muffler diffuser is presented as a function of frequency. The deviation of the characteristics of a “lossy” diffuser from this upper limit depends on the attenuation and regeneration characteristics of the acoustical elements in the muffler. These characteristics are investigated for the special element consisting of a perforated sheet, and the results are applied to an analysis of the insertion loss of a muffler diffuser of the perforated basket type.
31(1959); http://dx.doi.org/10.1121/1.1907850View Description Hide Description
The experiments described deal mainly with the propagation of continuous waves of a particular frequency, and with the variation of signal strength with the depth of the receiver and the water using “point,” almost nondirectional, transducers. A simple method has been found for lining experimental model scale tanks to make them anechoic at the frequencies considered. It has been demonstrated that temperature changes and surfacewaves produce marked changes in sound propagation. More important influences, however, appear to be due to the nature of the bottom and the depth of the water.
Point‐by‐point observations, described in Sec. II of the paper, indicate that multiple reflections between the water surface and a hard reflecting bottom, like steel or concrete, result in the propagation of many of the higher modes or orders of reflection and the records of sound intensity variation from surface to bottom is covered with rubber (equivalent to mud and sand), however, the higher modes are suppressed and the records of surface to bottom intensifies are much simpler, containing relatively few maxima and minima. All these observations are in reasonable accord with either the mode theory or the ray theory.
It has been demonstrated also that the received signal (in all‐round transmission and reception) is extremely sensitive to the depth of water. A change of depth of say 5 ft in water of depth 200 ft (full scale) may result in a change of the order of 30 db in received signal.
The distribution of the sound field on the bottom and surface of a water layer has been demonstrated by using sounds of relatively high intensity (Sec. III). Interference patterns form not only on the bottom but also on the surface of the water. A simple “abrasive” method has been devised which provides a permanent record of the sound pattern on the bottom.
A new scanning technique has been developed which gives a complete picture of a sound field of relatively low intensity, in a vertical plane either longitudinal or transverse in the water (Sec. IV) . In this method “point” transducers are used, one of which scans a vertical line several times a second whilst the other travels along or across the tank at a predetermined depth. The received signal modulates the cathode‐ray oscilloscope spot which moves up and down in synchronism with the scanning transducer. The scan patterns reveal a striking difference between the two cases of a hard steel (rock) bottom and a rubber covered (mud and sand) bottom. The pattern for a steel bottom is very complex and contains many maxima and minima in each vertical scan. The rubber bottom, on the other hand, provides only a few maxima and minima at each scan. The patterns hitherto obtained are, however, not amenable to mathematical treatment. They confirm and amplify the results obtained by point‐to‐point methods described in Sec. II.
This method of scanning should prove a useful tool for further studies of low‐intensity sound fields in water.
31(1959); http://dx.doi.org/10.1121/1.1907851View Description Hide Description
An attempt has been made to show that (1) the rotating tones in hearing, (2) the rotating vibrations on the skin, (3) the difference limen for the smallest perceptible distance on the skin, and (4) Mach's law of contrast are all a consequence of the same funneling action of the nervous system. In many situations the role of the funneling action can be better understood if a neural funneling unit is proposed, taking into account that a local stimulus produces both an area of activity and, around it, an area of decreased sensitivity. Since the inner and outer hair cells in the cochlea show a difference in sensitivity, the funneling action between these areas of different sensitivity has been investigated. It has been found that, between such areas, the locus of the sensation is continuously displaced as the intensity of the stimulus is increased. This suggests that along the organ of Corti there is a longitudinal displacement produced by variations in frequency, and a radial displacement between the outer and inner hair cells produced by variations in sound pressure. Thus there seems to be a pitch‐loudness coordinate system in the ear. The cochlear model (described earlier) with nerve supply was therefore further developed into a cochlear model with more and less sensitive nerve supplies, in order to represent the outer and inner hair cells in the organ of Corti.
31(1959); http://dx.doi.org/10.1121/1.1907852View Description Hide Description
The identification of different interaural correlations was examined over a range of reference correlations. Interaural correlations were produced by the method of Licklider and Dzendolet in which three independent noise sources were combined into two outputs. The change in interaural correlation (squared) required for 75% correct identification varied from about 0.4 for a reference correlation of 0.0 to about 0.04 for a reference correlation of 1.0.
31(1959); http://dx.doi.org/10.1121/1.1907853View Description Hide Description
In a previous study it was proposed that tonal masking arose mainly from the cochlear activity pattern of the masking tone, modified by the formation of beats between the signal and masking tones. The present study casts further light on these proposed mechanisms by comparing the masking effects of pure tones of 500, 1000, 2000, and 4000 cps at 60 and 80 db SL with bands of noise of equal intensities and centered at the same frequencies. The results show that the noise bands produce about the same amount of extended masking despite the absence of any possible aural harmonic distortion, but greater direct masking due to the elimination of beats. Furthermore, the noise‐masking curves join the tone‐masking curves at the second peak in the latter, providing strong additional support for the proposed mechanisms of auditory masking.
31(1959); http://dx.doi.org/10.1121/1.1907854View Description Hide Description
Comparisons were made by numerous observers of the stereophonic perception of direct versus reflected sound. For conventional direct sound, two loudspeakers having wide frequency response were used at spacings of from six to fifteen feet, directed towards the listeners. For reflected sound, equivalent dual sound sources were used placed back‐to‐back near the walls of a room in which it was desired to establish a stereophonic sound field. The frequency response of the latter system was equalized to have the same apparent response as the conventional system.
Many of the tests were conducted behind a sound permeable screen. Listeners were mixed in their ability to identify the reflective system and in their preference for one system over the other, although they reacted favorably to both systems.
31(1959); http://dx.doi.org/10.1121/1.1907855View Description Hide Description
Speech intelligibility was tested in a low‐frequency masking noise. Various conditions of speech and noise filtering below 1200 cps were employed in order to test the relative effects of direct low‐frequency masking and upward spread of masking to higher frequency regions. Tests were carried out at three noise spectrum levels which corresponded to overall unfiltered levels of 85, 105, and 115 db. The results showed significant decreases in intelligibility as the noise energy was admitted progressively between 300 and 20 cps. Further, the speech frequencies between 20 and 300 cps provided no significant contribution to intelligibility under any noise condition tested. It is, therefore, concluded that the low frequency energy in the noise produced upward spread of masking. This interpretation is reinforced by the fact that spread of masking was greater at higher noise levels and also at lower speech‐to‐noise ratios. Implications for calculating the effects of noise interference upon intelligibility are discussed.
- LETTERS TO THE EDITOR
31(1959); http://dx.doi.org/10.1121/1.1907857View Description Hide Description
Note on Finite Amplitude Propagation Effects on Shock Wave Travel Times from Explosions at High Altitude31(1959); http://dx.doi.org/10.1121/1.1907858View Description Hide Description