Contains reports on six research projects.National Science Foundation (Grant G-9330)United States Navy, Office of Naval Research (Contract Nonr-1841(42)

Ball, N. A.

Dean, L. W., III

Ingard, K. Uno

Maling, G. C., Jr.

Wiley, D. S.

DSpace@MIT

X. PHYSICAL ACOUSTICSProf. K. U. Ingard N. A. Ball E. J. Martens, Jr.Dr. L. W. Dean III G. C. Maling, Jr. D. S. WileyDr. R. G. Chatterji H. L. Willke, Jr.A. A LOW RESONANT FREQUENCY BARIUM TITANATE TRANSDUCERA barium titanate slab with a resonant frequency of 1000 cps would be 2. 5 metersthick. Therefore, if one wants a resonant transducer at lower frequencies, one mustfind some way to lower the resonant frequency of a piece of barium titanate of reasonabledimensions.One approach to the problem is the configuration shown in Fig. X-1. Two strips ofbarium titanate are cemented together to form a bilaminate, which bends when a voltageis applied across the faces. The resonant frequency is lowered by the addition of massesto the ends. Transducers having resonant frequencies from 100 cps to 2000 cps weremade from barium titanate bilaminates 6 cm long, 3 cm wide, and 1/3-1 cm thick byadding end masses of approximately 100-200 grams.BARIUM TITANATE CERAMIC(BIL I NATE)E-- LECTRICAL CONI:ECTIONSTO SILVERD FACESOF CERAMICFig. X-1. A mass-loaded bar.Attempts to find a simple formula relating the resonant frequency to the transducerparameters have failed. However, by adding or subtracting mass from the ends, thedevice can be tuned to a particular frequency.Since the transducer is physically much smaller than a wavelength of sound at itsresonance, it does not make an efficient radiator. For such a device the radiationimpedance of various media does not scale as pc, where p is the density, and c thespeed of sound, but as pc - (ka) 4 , where k is the wave number (k=w/c), and a is a char-acteristic dimension of the transducer. Thus this device is a less efficient radiator inwater than it is in air. The radiation pattern, as expected, is that of a dipole, the axisThis work was supported in part by the U. S. Navy (Office of Naval Research) underContract Nonr-1841(42).131(X. PHYSICAL ACOUSTICS)of which is perpendicular to the flat surface of the bilaminate.Details of measurements of the electrical and mechanical parameters are given1in N. A. Ball's thesis.N. A. Ball, L. W. Dean IIIReferences1. N. A. Ball, Determination of Design Parameters for a Novel ElectroacousticalTransducer, S. M. Thesis, Department of Electrical Engineering, M. I. T. , June 1961.B. THE DAMPING OF MECHANICAL OSCILLATORS BY FLOWA low-speed wind tunnel has been constructed in order to make measurements onthe damping of mass-spring oscillators by flow. The damping of an oscillator has beenfound to be a strong function of flow velocity. For example, the amplitude of an oscil-lator with a period of 1. 04 seconds decreases to one-half of its original value with noflow in 6 minutes and 37 seconds. A flow velocity of 200 feet per minute past the masscauses this damping time to decrease to 1 minute and 27 seconds.Results of this kind can be most easily interpreted by using the following analysis:The force on the mass isF = K(V-u) , (1)where V is the air stream velocity, u is the velocity of the mass, and K is some pro-portionality factor. In practice, u can be made much less than V so that, apart froma steady force that shifts the equilibrium position slightly, the drag force may be writtenF = 2KVu. (2)The drag force is therefore proportional to the oscillator velocity and should resultin ordinary exponential damping. The dependence (if any) of K on oscillator frequencyand flow speed can be found by measurement of the damping time. The experimentsthat have been performed, thus far, have not given particularly satisfactory resultsbecause disk-shaped weights were used to change the mass, and therefore the periodof the oscillator. In the next series of experiments, the mass will be a sphere, andthe period will be changed by changing the spring constant.U. Ingard, G. C. Maling, Jr.C. ACOUSTICS OF INHOMOGENEOUS MOVING MEDIATwo problems that involve acoustic wave propagation in inhomogeneous media arebeing investigated. The first involves the effect of a plane boundary on the magnitude132(X. PHYSICAL ACOUSTICS)of the fluctuations in sound pressure that occur when a slowly moving turbulent airstream is made to pass over the boundary.This problem has been analyzed theoretically and an experiment is now being carriedout in the anechoic chamber to study the problem further. Construction of the experi-mental apparatus has now been completed and data are being obtained.Another aspect of the interaction of sound with moving air streams involves the influ-ence of a heat source in a moving medium. Through the modulation of the heat transferto the medium by the sound itself, the heat source acts as a scatterer of sound. Theconditions for self-sustained oscillations (as in the Rijke tube) are being investigatedwith particular emphasis on the amplitude of the oscillations as a function of geometry,heat-source parameters, and so forth. The effect has been observed in a number ofRijke tubes of various sizes, but quantitative data have not yet been obtained becauseof difficulties involved in the construction of a heat source that will introduce heat intothe medium at a known rate.G. C. Maling, Jr.D. BIFURCATION INSTABILITY OF A LIQUID CONDUCTOR IN AN AXIALMAGNETIC FIELD*During the past year, an extensive series of experiments has been performed tostudy the instability of a mercury current filament moving in an axial constant magneticFig. 2. Illustration of self-pinch of a mercurycolumn falling freely under gravity,and carrying a current of 180 amp.The diameter of the mercury columnis 0. 3 cm.*This work was supported in part by the National Science Foundation underGrant G-9330.133Illustration of spiral instability of a mercury column fallingunder gravity in an axial magnetic field. The diameter ofthe mercury column is 0. 5 cm; the electrical current throughit, 80 amps; and the axial magnetic field, 2200 gauss. Noticethat the cross section of the mercury column is deformedas it spirals and that there is an indication of bifurcation.Actually, judging from the reflected light pattern at point P,two indentations seem to be present in the stream.Fig. X-4. Illustration of a fully developedbifurcation resulting from spiralinstability in a mercury columnmoving in an axial magnetic field.The diameter of the column is0. 5 cm; the current through it,260 amps; and the magnetic field,3600 gauss.134Fig. X-3.(X. PHYSICAL ACOUSTICS)field. The pinch instability of this mercury filament (with no magnetic field present),and the spiral instability, have been studied and photographed by means of high-speedphotography. A typical example of pictures showing pinch and spiral instabilities isshown in Figs. X-2 and X-3. During the course of these studies a new type of instabilitywas found which might be referred to as a "bifurcation instability," and is illustratedin the photograph in Fig. X-4. At sufficiently large magnetic fields it was found thatthe mercury stream divides in two, continuing to spiral about the magnetic field. Thisbifurcation results presumably from the fact that when the mercury column bends, itscross section changes from circular to elliptical, and this distortion of the cross sec-tion continues until the stream divides in two. A detailed account of these experimentsis being prepared for publication.D. S. Wiley, U. IngardE. SEARCH FOR A STABLE PINCH IN A HORIZONTAL MERCURY COLUMNIn the first published account1 of the pinch phenomenon in a liquid conductor, andin a later systematic study of this phenomenon, it was indicated that a stable pinch canbe obtained in a horizontal mercury column that is carrying an electric current. Thispinch, which formed a V-shaped indentation on the free surface of the mercury, wasclaimed to be stable and to increase in depth with the current. A theoretical study ofthis problem has been undertaken, and it has been shown that, at least for an infinitelylong horizontal mercury column, a pinch cannot be explained. Experiments have beenperformed to study this phenomenon by using a mercury column in a vertical tray con-sisting of lucite plates. The thickness of the column was approximately 0. 5 inch, thelength was approximately 10 inches, and the height was varied from 0. 5 inch to 3 inches.Currents up to 2000 amps were used. No pinches were found. Pinchlike deformationsof the free surface of the mercury could be obtained, however, if the electric leads tothe column were asymmetrical and hence produced asymmetry in the magnetic field,and it is clear that in experiments of this type special care should be taken to avoidinhomogeneities in the magnetic field. When such inhomogeneities are produced inten-tionally by ferromagnetic materials placed above the mercury columns, steady defor-mations of the free-mercury surface are readily produced.U. Ingard, D. S. WileyReferences1. C. Hering, A practical limitation of resistance furnaces, the Pinch Phenomenon,Trans. Am. Electrochem. Soc., Vol. XI, p. 329, 1907.*This work was supported in part by the National Science Foundation underGrant G-9330.135(X. PHYSICAL ACOUSTICS)2. E. E. Northrup, Some newly observed manifestations of forces in the interiorof an electric conductor, Phys. Rev. 24, 474 (1907).F. OSCILLATION OF A FERROMAGNETIC BODY INSIDE A LIQUID CONDUCTORIn the course of our studies of instabilities of a mercury column, an amusing effectwas found by floating a piece of metal on the surface of a horizontal mercury column.When a current (of approximately 1000 amps) was sent through the column, the pieceof iron was pulled into the mercury and set into vertical oscillations approximately aboutthe center of the mercury column. At the center of the column the magnetic field isclearly zero and the vertical field gradients on either side are directed toward the centerline, thereby producing a linear restoring force on the piece of iron.U. Ingard, D. S. WileyThis work was supported in part by the National Science Foundation underGrant G-9330.136

Physical Acoustics

http://dspace.mit.edu/bitstream/1721.1/53627/1/RLE_QPR_063_X.pdf

Physical Acoustics

Abstract

Similar works

Full text

Available Versions

DSpace@MIT