Volume 59, Issue 5, May 1976
Index of content:
59(1976); http://dx.doi.org/10.1121/1.380967View Description Hide Description
A general solution for the sound radiated from a circular pipe having an arbitrary inside profile of orifice is obtained by the use of Laplace transforms and the Wiener–Hopf technique. The pipe may include vibrating surfaces. Results are calculated for the velocity potential at a large distance from the orifice and for the reflection coefficient for the dominant‐mode component of the velocity potential in the pipe. The solution is applicable, for example, to the design of an acoustic transducer, and for noise control from the orifice. Some numerical results for the velocity potential of a modelloudspeaker and for the excess attenuation of a muffler near the open end of a pipe are presented graphically.
Subject Classification:20.55, 20.15.
59(1976); http://dx.doi.org/10.1121/1.380968View Description Hide Description
It is shown that by appropriately processing the output signals of the elements in a symmetric array, a tilted sum pattern or difference pattern can be produced without numerous delay lines or phase‐shift networks. The tilted pattern is achieved by combining, in proper phase, two outputs of an array; the first output is that of a particular amplitude weighted phase‐symmetric array while the second is that of a particular amplitude weighted phase‐antisymmetric array. To achieve the proper phase relationship between these two outputs, one of them must be phase shifted by ±90°. Theoretical calculations and experimental results are presented for the case of a line array of nine elements that are equally spaced a half‐wavelength apart; both a sum pattern and a difference pattern tilted to 30° from the normal to the line array, by this method, are shown. The variation of the side‐lobe levels of these tilted patterns is examined as the ±90° phase shift is perturbed. The possibility of using this technique to continuously vary the angle of tilt is discussed.
Subject Classification: 20.55; 30.50; 60.30; 35.54.
59(1976); http://dx.doi.org/10.1121/1.380969View Description Hide Description
A theory of the spectral analysis of the scattering of elastic waves is presented and illustrated with numerical results for the scattering by a circular cylindrical fluid inclusion in a solid. When the spectral frequencies are nearly equal to the real parts of the principal frequencies of the fluid inclusion in free vibration, the power spectrum of the scattered pulses undergoes a rapid rise and fall in magnitude because of the selective transmission of an incident wave. The conspicuous peaks and valleys of the backward and forward scattering spectra can be identified with the overtone frequencies of the two lowest normal modes of the cylinder, from which the characteristics of the fluid inclusion, the ratio of the wave speed to radius, can be determined.
Subject Classification: 20.15, 20.30.
59(1976); http://dx.doi.org/10.1121/1.380970View Description Hide Description
The reflection and transmission of plane harmonic waves impinging from air to the plane face of porous material occupying a semi‐infinite space as well as with finite thickness is considered. The variation of these coefficients with the angle of incidence and various parameters (frequency, permeability, etc.) is illustrated for certain porous materials. The results obtained indicate that the transmission coefficient remains the same under the assumption of velocity potential (there is no velocity potential in general in the porous material) while the reflection coefficient changes significantly.
Subject Classification: 20.30, 20.35.
59(1976); http://dx.doi.org/10.1121/1.380971View Description Hide Description
An analysis is presented of the sound propagation and attenuation in a circular duct carrying a uniform mean flow and lined with an anisotropicporous material backed by cellular cavities. A combination of a fourth‐order Runge–Kutta routine and a Newton–Raphson procedure is used to determine the effects of the liner properties, the flowMach number, and the sound frequency on the attenuation of spinning and nonspinning modes. The results show that low‐frequency noise is better attenuated by anisotropic liners. The optimum liner is the one whose axial resistivity increases with increasing frequency.
Subject Classification: 20.45, 20.35; 50.40.
59(1976); http://dx.doi.org/10.1121/1.380972View Description Hide Description
The sound absorption performance of an acoustic absorber consisting of a stretched circular membrane placed a short distance in front of a fiberglass blanket was both measured and predicted. Both theoretical and experimental analyses were restricted to plane acoustic waves. Theoretical predictions indicated that the membrane–blanket combination would have a sound powerabsorption coefficient nearly equal to the sound powerabsorption coefficient of the blanket alone if the incident acoustic plane wave drove the membrane at one of its resonance frequencies. Theoretical analysis also predicted that the sound powerabsorption coefficient would approach zero when the membrane was driven at an antiresonance frequency by the incident acoustic plane wave. Experimental agreement with theoretical predictions was good for several membrane–blanket combinations. The results show that membrane–blanket combinations can be effective acoustic absorbers in frequency ranges which do not include the antiresonance frequencies of the membrane. The equations developed may be used to predict the acoustic performance of any membrane–blanket combination.
Subect Classification: 20.30, 20.60; 40.20.
Radiation of difference‐frequency sound generated by nonlinear interaction in a silicone rubber cylinder59(1976); http://dx.doi.org/10.1121/1.380973View Description Hide Description
In this paper we describe an experimental and theoretical investigation of the parametric signal generated in one medium, a silicone rubber cylinder, and radiated into a second medium, water. The primary waves (∠1.4 MHz) are confined to a narrow region around the axis of the cylinder and, because of the relatively high absorption at these frequencies, are largely attenuated before reaching the end of the cylinder. The silicone rubber cylinder serves two purposes. First, the low sound speed (∠1000 m/sec) and high parameter of nonlinearity (1+B/2A?5) of the silicone rubber makes the virtual sources more than seven times as strong as they would be in water. Second, because the sound speed in silicone rubber is less than that of the surrounding water, the silicone rubber cylinder acts as a slow waveguide antenna for the difference‐frequency waves. The system is analyzed by numerically solving the system of equations obtained by coupling the surface Helmholtz integral equation for the interior of the silicone cylinder (which includes the virtual sourcesI with the integral equation for the region exterior to the cylinder. Experimental results obtained for difference frequencies between 10 and 20 kHz compare favorably with theory.
Subject Classification: 25.35, 25.15; 30.75.
59(1976); http://dx.doi.org/10.1121/1.380962View Description Hide Description
Absolute measurements of the amplitude of the first four harmonicof 30‐MHz finite amplitude ultrasonic waves are reported for fused silica samples of various lengths and for aluminumsingle crystals with different amounts of cold work. The harmonically distorted motion of the end of the sample is detected by a capacity microphone and the individual harmonics are then selected and amplified by a heterodyne receiver with flat frequency response from 30 to 250 MHz. The fused silica data are found to be in excellent agreement with a model of Fubini, originally developed for gases, which for solids depends on the second‐ and third‐order elastic constants but none of the higher constants. A discussion is presented of the reasons for the insensitivity of the measurements to the values of the fourth‐ and higher‐order elastic constants. Agreement with the model of Fubinin is not observed in single crystalaluminum. The quantitative differences are not fully consistent with existing models for dislocation contributions to harmonic generation.
Subject Classification: 25.15, 25.20; 35.26; 25.25.
59(1976); http://dx.doi.org/10.1121/1.380963View Description Hide Description
This paper presents the results of an experimental study of hydrodynamic noise conducted in the High‐Speed Water Tunnel of the California Institute of Technology. The objective of the test program was to measure some of the basic characteristics of noise radiated from submerged hydrofoils, both fully wetted and cavitating. Measurements of fully wetted hydrodynamic noise are difficult to make due to the low intensities, but the very low background noise level of the Caltech tunnel makes it possible to measure this noise under some conditions. An increase in the angle of attack of a hydrofoil was found to produce a slight increase in noise spectrum level at high frequencies. An increase in surface roughness produced a more significant increase over a wider frequency range. Noise was measured for three distinct types of hydrofoil cavitation: blade surface cavitation, wake cavitation, and trailing vortexcavitation. Foil vibration was found to be important in blade surface cavitation, but not in the other forms. Both blade surface and wake cavitation have spectral peaks at a Strouhal number based on a cavity length of 0.5. Trailing vortexcavitation is found to be a relatively weak source of noise, owing to the fact that in the water tunnel this type of cavitation is gaseous in nature.
Subject Classification: 30.70, 30.85, 30.50.
59(1976); http://dx.doi.org/10.1121/1.380964View Description Hide Description
A successful short focal length radar lens design technique was adapted to the problem of nonspherical thin underwater acoustic lens development and construction. The motivation was furnished by the many sonar requirements for small size lenses capable of operation in a scanning mode. The paper includes a discussion of the computer‐aided lens design, the fabrication of casting molds, the vacuum casting process, and the pattern and gain measurements on the final rubberlenses. The design was accomplished using a lens size and frequency that would be compatible with the test tank available for the work. the lenses constructed were about 7 in. in diameter, vacuum cast from 3120 RTV rubber, and were tested using an acoustic frequency of 185 KHz. The useful scanning range of the lens in these tests turned out to be ±20° from the axis. The gain of the lens was 20 dB, the main lobe beam width about 4°, and ths side lobes were from 12 to 19 dB below the main lobe. Total absorption and reflection losses were less than 1 dB. The F number of the lens was about 1.3.
Subject Classification: 30.80, 30.82, 30.25.
59(1976); http://dx.doi.org/10.1121/1.380965View Description Hide Description
An environmental/acoustic model of sound propagation in the Arctic Ocean, which accounts for reflection losses from ridged sea ice, has been developed. In this model sea‐ice ridges are represented as infinitely long, randomly distributed, elliptical half‐cylinders. Under‐ice reflection losses for acoustic wavelengths either large or small compared to ridge dimensions are computed from theoretical equations as a function of average keel depth and width, number of ridges/km, and grazing angle. Numerical values of under‐ice reflection loss as a function of grazing angle are then incorporated into ray‐theoretical computations of transmission loss assuming a single sound‐ speed profile which is characteristic of the central Arctic Ocean. The validity of the concepts and approximations, the limitations of the model, and the accuracy of coincident measurements of environmental and acoustic parameters required to validate the model are discussed. To illustrate the predictions and accuracy of the model under diverse ice conditions, several comparisons of theoretical and experimental determinations of under‐ice transmission loss in the central Arctic Ocean are presented. Midwater absorption loss, a complicating feature of transmission loss measurements at high frequencies, is also considered.
Subject Classification: 30.20, 30.30.
Interpretation of multipath scintillations Eleuthera to Bermuda in terms of internal waves and tides59(1976); http://dx.doi.org/10.1121/1.380966View Description Hide Description
Rate‐of‐phase and intensity spectra due to time‐varying m u l t i p a t h interference depend essentially on a single parameter ν2 which can be interpreted as the mean‐square rate‐of‐phase for any typical s i n g l e path. MIMI 406‐Hz phase and intensities are consistent with ν−1=270 and 357 sec for Eleuthera to Bermuda and Eleuthera to midstation transmissions, respectively, compared to 192 and 286 sec from a ray‐geometric calculation using an internal wave model based on oceanographic observations. Internal tides play a significant but not dominant role.
Subject Classification: 30.20, 30.35.
59(1976); http://dx.doi.org/10.1121/1.380974View Description Hide Description
Acoustic charges were detonated on a line normal to the Gulf Stream and recorded near Bermuda. Received signals were analyzed in one‐third‐octave bands from 40 to 200 Hz and analyzed for rms value over an 8‐sec period. Results indicate areas of low transmission associated with the North and South Walls of the stream that ranged between 4–10 dB. Highest levels were received from charges detonated north of the stream. These results can possibly be explained by varying sonic‐layer depths and a deepening sound channel axis between Slope Water and deep warm layers of Sargasso Sea water. Other factors possibly related to received amplitude fluctuation may be internal waves and ’’patches’’ of water different from surrounding areas. Further experiments using cw sounds are being planned to delineate seasonal and angular factors.
Subject Classification: 30.20, 30.25.
59(1976); http://dx.doi.org/10.1121/1.380975View Description Hide Description
A theory, which is suitable for making estimates of the acoustic field radiating from either a completely coherent (i.e., deterministic) or a partially coherent source is derived and discussed. The theory outputs are measures of beam bending and spreading due to refraction and diffraction. For the random source problem, the theory also provides estimates of the coherence of signals received by pairs of spatially separated hydrophones. The theory is based on an approximation that may nominally be termed parabolic. The limits of validity of the various approximations are discussed and a solution algorithm, which might be classified as an extended ray‐trace algorithm, is presented. A special case, in which this algorithm can be carried out analytically, is dicussed.
Subject Classification: 30.20; 60.20; 30.35; 20.30.
59(1976); http://dx.doi.org/10.1121/1.380976View Description Hide Description
The propagation paths from shallow explosive sources to a SOFAR axial receiver are determined by analyzingmeasured shot signatures. The charges were detonated along a 2800‐km track between Antigua and Newfoundland. Propagation was through several distinct water masses, each of which produced different observable effects on the shot signature. Because of the shallow depth of the source, the number of turning points below the SOFAR axis is the prime determinant of the time dispersion of the arrivals and is a convenient basis for classifying them. The range dependence of the dispersed arrivals depends on the large‐scale oceanography and discloses the identity of the ray paths which produce it.
Subject Classification: 30.20.
59(1976); http://dx.doi.org/10.1121/1.380977View Description Hide Description
Hollow glass spheres of various sizes have been preweakened to implode at ocean depths of approximately 3 km and sunk using chain weight. Acoustic signalsgenerated from the implosion of these spheres have been analyzed.Pressure signatures, energy‐density spectra, and total acoustic energy in the frequency band 96–5000 Hz are presented. The signatures of all the implosions have many features in common. Basically each consists of a low flat negative‐pressure pulse followed by a sharp positive‐pressure spike of roughly 0.2‐msec duration. The efficiency of the conversion of available potential energy to radiated acoustic energy is approximately 18%. Total radiated acoustic energy for spheres of 43.2‐cm diameter imploding at a 3‐km depth is about 53 dB r e 1 J. Preweakened glass spheres show promise as a tool in the study of the sedimentary structure of the ocean bottom due to the impulsive character of the signal that is radiated upon implosion.
Subject Classification: 30.50, 30.60, 30.70.
59(1976); http://dx.doi.org/10.1121/1.380978View Description Hide Description
Leaky wave poles are defined as those singularities of the acoustic admittance of a fluid‐loaded infinite plate that are located on the bottom Riemann sheet of the complex wavenumber plane and can appear near the saddle point of the complex path of steepest descent. These poles are shown to represent only the real, propagating modes in an unloaded plate. It is shown that for a point or line excited plate the value of leaky wave poles and their location relative to the saddle point are sufficient parameters to explicitly describe the acoustic radiation from submerged plates. This paper analyzes the leaky wave poles of both the Timoshenko–Mindlin plate equation and the classical plate equation.
Subject Classification: 30.50; 40.24.
59(1976); http://dx.doi.org/10.1121/1.380979View Description Hide Description
Leaky wave poles are defined as those singularities of the acoustic admittance of a fluid‐loaded infinite plate that are located on the bottom Riemann sheet of the complex wave number plane and can appear near the saddle point of the complex path of steepest descent. These poles represent only the real, propagating modes in an unloaded plate. It is shown that for a point or line‐excited fluid‐loaded classical and Timoshenko–Mindlin plate, the value of leaky wave poles and their location relative to the saddle point are sufficient parameters to explicitly describe the radiated power, the angle, beamwidth, amplitude, and existence of the radiation lobes, and the effect of structural damping on the radiation field.
Subject Classification: 30.50; 40.24.
59(1976); http://dx.doi.org/10.1121/1.380980View Description Hide Description
Normal‐mode analysis of underwater sound propagation in principle requires knowledge of pertinent physical parameters at all depths in the water and the bottom material—an unattainable omniscience. We present a method for determining the maximum depth to which this knowledge is necessary in order to hold the fractional errors in mode eigenvalues to prescribed limits. Let h n represent a vertical distance below the lower turning point of the nth‐mode solution. Insertion or removal of a horizontal plane reflector, at this depth, alters the mode eigenfunction and therefore the eigenvalueE n . The fractional error ΔE n /E n is a calculable function of h n ; this error being stipulated, h n can be found. The calculation need be made only for the highest mode that contributes significantly. Conversely, if all parameters are known to depth h, the consequent errors can be found. Two examples are analyzed, with simplifying restrictions: deep isovelocity water, low frequencies, many modes, bottoms that are isovelocity (the Pekeris case) or have a positive gradient of sound speed. For fractional errors of 10−4 to 10−6, h is a few acoustic wavelengths. In each example, bottom absorption has little effect on the result.
Subject Classification: 30.20, 30.50, 30.25.
59(1976); http://dx.doi.org/10.1121/1.380981View Description Hide Description
A nonlinear equation describing the motion of a nonlinear oscillator has been reduced by proper substitution to an integro‐differential equation and then solved by means of an iterative technique for an arbitrary forcing function. The effect of the nonlinear terms on the convergence has been studied. It has been shown that such a solution converges sectionally in an interval Δτ. An inequality has been determined which yields a maximum Δτ regardless of the form of the forcing function if ε=0. However, for a nonzero ε the interval of convergence is highly dependent of the form of the forcing function.
Subject Classification: 40.30, 40.20.