Volume 46, Issue 1B, July 1969

The Physics of Flow Noise
View Description Hide DescriptionThe nearfield flow noise that is generated in the boundary layer of a vehicle in water turns out to be practically, independent of the kind of vehicle that generates the turbulence. Recorded levels depend on the size and shape of the recording hydrophone, even at very low frequencies when the linear dimensions of the hydrophone are small as compared to the convection wavelength of the turbulence. At high frequencies, because of their finite size, all hydrophones become nearfield insensitive and record the radiated noise. No significant difference was observed in the radiated‐noise curve measured at a distance of about 100 ft from a rising buoyant unit, not even at frequencies as low as 150 Hz, whether the unit was of solid wood or had a thin metal shell. The radiation field depends on the second time derivative of the turbulent velocity fluctuations and, consequently, on the unsteadiness and intermittancy of the turbulence in the boundary layer. For a rotating cylinder, the measured radiation field levels approach those predicted by the recently improved Lighthill formula. For a ship, they are higher; for a buoyant unit, which is a small and a very unstable vehicle, the radiated noise becomes particularly great.

Sound Velocity and Absorption in Low‐Pressure Gases Confined to Tubes of Circular Cross Section
View Description Hide DescriptionThe propagation constant for sound waves propagated through gases confined to tubes is shown to be a function of the specific heat of the gas, a “Reynolds” number, a “Knudsen” number, and the momentum and energy accommodation coefficients of the surface. A numerical solution for the propagation constant agrees with room temperature velocity and absorptionmeasurements in Ar and assuming a momentum accommodation coefficient of 1 and an energy accommodation coefficient of 0.9. No effort was made to clean the tube‐wall surface, and no difference could be detected in a stainless steel and a brass tube. The method offers considerable promise for measuring energy accommodation coefficients.

Asymmetries in Cylindrical Waveguides
View Description Hide DescriptionCylindrical geometries with axial symmetry are often used to model physical systems. Although such a model materially simplifies calculations, it may ignore significant effects arising from small asymmetries in the system. In order to demonstrate this and to examine the nature of such effects, a model was analyzed consisting of a cylindrical waveguide with perfectly reflecting walls and an isolated point source displaced small distance from the axis of the hole. The subsequent analysis shows two distinct types of arrivals associated with the geometry. Both of these produce strikingly large asymmetries in the motion of the system. These effects are clearly displayed in the closed‐form solutions obtained for the problem and the light that they shed on the nature of the reflection process at a cylindrical interface may well be of significant value for ray‐theory methods in diffraction.

Effect of a Shear Layer on Plane Waves of Sound in a Fluid
View Description Hide DescriptionAvailable theory indicates that plane waves of sound are reflected and refracted at an interface of relative motion (a velocity discontinuity) between two regions of fluid. If the relative velocity is sufficiently great, three types of reflection occur, ordinary, total, and amplified, depending on the incident wave angle. In the amplification regime, theory predicts resonances. Here the velocity discontinuity replaced by a transition layer of finite thickness separating the two fluid regions. This layer is approximated by two equal velocity discontinuities (Model I) and by a linear velocity profile shear layer (Model II). For one example in the regime of ordinary reflection, the effects of thickness are negligible for thicknesses up to 1/10 of the incident wavelength. For the chosen examples in amplified reflection, extreme reductions in transmission and reflection coefficients occur for a thickness as little as 1/50 of a wavelength. The two models approach (at unequal rates) total reflection and zero transmission at larger thicknesses. These effects are produced by layers of fluid traveling at or near the apparent wave speed parallel to the shear layer. Such layers tend to “insulate” the two fluid regions from each other.

Free Vibrations of Ring‐ and‐Stringer‐Stiffened Conical Shells
View Description Hide DescriptionStrain‐displacement relations are developed for a thin truncated circular conical shell and its reinforcing rings and stringers. Using these relations in an energy approach, methods are developed for determining the resonant frequencies of simply‐supported conical shells in unstiffened, ring stiffened, or ring‐and‐stringer‐stiffened configurations. The stiffeners may be either widely separated or closely spaced. Computed values obtained using these methods are compared with the results of a series of experiments on ring‐stiffened and ring‐and‐stringer‐stiffened conical shells.

Vibrations of Fluid‐Filled Spherical Shells
View Description Hide DescriptionUtilizing linear shell theory, which includes both membrane and bending effects, the differential equations for the axisymmetric, nontorsional motion of a fluid‐filled thin spherical shell are obtained by means of Hamilton's principle. The motion of the fluid is assumed to be governed by the linear wave equation. It is shown that appropriate limiting cases of the frequency equation of a fluid‐filled shell agree with those of the simpler models previously investigated. A description of some of the salient features of the frequency spectrum of such a fluid‐shell system is also given in view of the frequency spectra of the limiting cases.

Vibration in an Infinite Isotropic Elastic Plate Due to a Vertical Harmonic Load
View Description Hide DescriptionAnalysis and numerical results are presented for a problem in which a vertical harmonic load is applied to an infinite isotropic elastic plate. Two cases are analyzed: In the first case, an equal harmonic load is applied to the two bounding planes of the plate in a rectangular region, and in the second case, a harmonic load is applied to the bottom face equal and opposite to the harmonic load on the upper face of the plate. In each case, the vertical displacement at the center of the loaded area is derived and numerical results are presented.

Intensity Fluctuations in Reflections from the Ocean Surface
View Description Hide DescriptionThe fluctuations in energy occurring in successive reflections of acoustic pings from the oceansurface have been measured in the acoustic frequency range from 160 to 1360 Hz. The relations of these fluctuations to the independently measured statistics of the ocean waves indicate that the degree of fluctuation is proportional to the effective roughnessR up to a saturation roughness, the distribution of reflected energies departs more and more strongly from normal as the roughness increases, and only surface waves whose wavelength exceeds that of the impinging acoustic ping by a factor considerably greater than I will produce fluctuations in the reflected pings.

Bubble Dynamics in a Non‐Newtonian Fluid Subject to Periodically Varying Pressures
View Description Hide DescriptionThis paper investigates the vibration characteristics of a small insoluble gas bubble in quiescent blood subject to harmonic pressure fluctuations close to the natural frequency. Pressure fluctuations of about 0.05, 0.1, and 0.2 of the mean pressure are studied. Results are obtained for the pressure variation of the blood in the vicinity of the bubble and for the changes of the mean radius and surface acceleration of the bubble. The resonance curves are calculated. It is disclosed that the effect of viscosity on the response is rather important in blood.

Acoustic Decoupling Properties of Onionskin Paper
View Description Hide DescriptionIt has been previously determined that precompressed onionskin paper may be used as an acoustic decoupler. In our evaluation, compressional‐wave measurements were made on various types of paper, and in particular onionskin typing paper, at 32 and 1000 kHz. At the lower frequency, a composite material technique was used to allow pressurization of the samples. The velocity of sound and attenuation were found to vary nonlinearly with pressure over the range from 0 to 2000 psi. This nonlinearity introduces a nonlinear acoustic loading of the transducer elements and is the main disadvantage of onionskin paper. However, it was confirmed that the onionskin paper should be more stable with pressure than the other papers, provided that it has been properly precompressed. Most of the insertion loss provided by onionskin paper is caused by the mismatch in acoustic impedance. Thus, a fairly wide variety of materials should provide equivalent acoustical properties.

Development of Simple Equations for Accurate and More Realistic Calculation of the Speed of Sound in Seawater
View Description Hide DescriptionMany equations for calculating the speed of sound in the sea suffer from a lack of accuracy in spite of their complexity. By taking an appropriate approach in the development of the equation and by limiting the data to be fitted to those that correspond to real seawater conditions, it is found that more simple and more accurate equations can be developed. A survey of the characteristics of all existing seawaters is first made. This leads to a substantial limitation in the existing data to be fitted and suggests the appropriate measurements for further research. Previous methods of formulation are then discussed and a new method presented. To illustrate the advantages of the latter method, two equations formulated in this way are given. One fits Wilson's second equation for seawater to within 0.1 m/sec in the domain described, and the other fits Wilson's corresponding data with a better accuracy than does Wilson's equation.

Experiments on the Acoustic Modulation of Large‐Amplitude Waves
View Description Hide DescriptionA series of experiments were preformed to study the parametric relationship between two high‐frequency carrier waves and the difference‐frequency wave created by their nonlinear interaction. The measurements were made in a freshwater lake in the farfield of all radiations. A split‐face piston projector, 2 in. × 2 in., was driven by two pulsed power amplifiers, and the resulting acoustic fields were measured with three separate calibrated hydrophones. Before the experiments were conducted, the usefulness of a frequency selective acoustic filter (SOAB) in identifying pseudosound was established. In the first experiments, a 143 kHz difference‐frequency wave having an extrapolated source level of 81 dB re 1 μbar at 1 yd was created from the nonlinear interaction of a 981‐kHz and a 1124‐kHz radiation whose source levels were 121 and 113 dB, respectively. The difference‐frequency sound propagated according to the spherical spreading law, independently of the existence of the carriers, with a 1.7° half‐power beamwidth. The difference‐frequency SPL was found to be proportional to the product of carrier‐wave amplitudes, except at high carrier‐wave source levels, and proportional to the difference frequency to a power of 1.7. With few exceptions, the results showed good agreement with a mathematical model of the problem devised by Westervelt.

Underwater Acoustic Propagation Prediction by the Alternating‐Direction Implicit‐Explicit Computational Method
View Description Hide DescriptionA computer solution of the wave‐difference equations is found by using an interlacing implicit‐explicit scheme. In the computation, the entire two‐dimensional field is found as a function of time. The examples considered involve propagation in a homogeneous shallow‐water channel, where the effect of superposition of discrete spectra produces characteristic modal patterns. The spatial sound‐pressure fluctuations are represented as plot‐density variations along the two‐dimensional channel. Examples of discrete propagated modes as well as evanescent modes are presented. The size of the field that can be presented is limited by the size, accuracy, and speed of the computer.

Transmission of Noise from a Turbulent Boundary Layer through a Flexible Plate into a Closed Cavity
View Description Hide DescriptionThe title problem is investigated, emphasizing two effects that are usually ignored in the literature. These are (i) nonlinear plate stiffness and (ii) mutual interaction between the plate and external and/or internal (cavity) air flow. The method of analysis employs modal expansions for the plate and cavity (air) motions, with the solution effected in the time (rather than the frequency) domain. The external flow‐pressure perturbations due to the plate motion are assumed to be described adequately by classical acoustic theoryincludingconvectioneffects. A discussion is given as to when the two effects will be important and a practical, numerical example is worked out to illustrate the method.

Measurements on the Effect of Transducer Size on the Resolution of Boundary‐Layer Pressure Fluctuations
View Description Hide DescriptionThe response of a flush‐mounted transducer to the pressure field in a turbulent boundary layer is known to depend on the spatial and temporal characteristics of the transducer. This paper presents an experimental study of this dependence. The reduced data are presented in a manner similar to that used by Corcos to present his estimation of the response of transducers to a corresponding pressure field.

Helmholtz Oscillations in Pulsating‐Combustion Chambers
View Description Hide DescriptionAn investigation has been made of the conditions under which liquid‐fueled pulsating‐combustion chambers operate as Helmholtz resonators. The experimental apparatus consists of a vertical, cylindrical combustion chamber that is partially filled with a liquid fuel and completely closed except for a single, sharp‐edge orifice in the top end. A manifold chamber and an exhaust pipe are mounted above the orifice. The pulsating‐combustion process operates on air drawn intermittently from a steady flow of air that is supplied through the manifold. Measurements have been made of chamber pressure as a function of time for various chamber configurations and exhaust‐pipe lengths. Results show that the mode of operation is either anharmonic or harmonic, depending on whether the exhaust‐pipe length is smaller or larger, respectively, than a critical transition length. The transition to harmonic operation is accompanied by a sudden jump in both frequency and pressure amplitude. Theoretical double‐cavity resonator frequencies agree well with experimental frequencies for the harmonic mode of operation but are larger than frequencies for anharmonic operation by factors of about two or greater. The harmonic mode of operation appears to be governed by a Helmholtz‐type mechanism, whereas the anharmonic mode is governed predominantly by heat‐transfer processes.

Attenuation of Guided, Weak Sawtooth Waves
View Description Hide DescriptionThis paper presents an analytical study of the decay of plane sawtooth waves traveling inside tubes. The analysis is based on energy considerations and takes into account the energy dissipated at the walls owing to heat and momentum transfer. The results are applicable to sawtooths with shock strengths δ in the range 0⩽δ≈0.1. Comparison with existing data [H. Medwin, J. Acoust. Soc. Amer. 36, 870–877 (1964)] shows good agreement within this range.
 LETTERS TO THE EDITOR


Interferometric Measurement of Ultrasonic Velocity in Liquids—Effect of Diffraction
View Description Hide DescriptionThe effect of diffraction on Sound‐velocity measurements in liquids was studied in the low frequency range, 0.6 to 3.0 MHz, using a single‐crystal interferometer. The excess velocity ΔC over the plane‐wave velocityC was found to follow the relation where λ is the wavelength, d the beam diameter, and D is the distance from the source at which measurements were made. The diffractioneffects are 3.2 times the values envisaged theoretically [from Bass and Williams cited in H. J. McSkimin, J. Acoust. Soc. Amer. 33, 539 (L) (1961)].

Application of the Fast Fourier Transform to Linear, Distributed System Response Calculations
View Description Hide DescriptionThe calculation of the response of a distributed system to a homogeneous random field involves the calculation of an integral of the form , where S(x − x′, ω) is the cross spectrum of the random field, and G(x _{0}, x,ω) is the system response function. Transformation to the spectral domain, (k − ω space), simplifies the integration and allows considerable savings in computational time. The fast Fourier transform technique can be readily applied to the problem, reducing the required time by more than an order of magnitude. An example of transducer resolution in boundary layer‐turbulence is presented.

Comments on Two Letters by Neubauer on Creeping and Circumferential Waves [J. Acoust. Soc. Amer. 44, 298(L) (1968); 1150(L) (1968)]
View Description Hide DescriptionNeubauer has offered some interesting circumstantial evidence for the existence of several surface waves. However, there remain discrepancies between his results and known theory. He must also present stronger evidence than that given to discriminate between his surface waves and other phenomena explainable by the same data. His use of the schlieren technique is very promising, but he does not take full advantage of its potential.
