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Submitted on 1 Jan 1978
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FOURTH SOUND HELMHOLTZ RESONATOR IN
SUPERFLUID 3He
T. Chainer, Y. Morii, H. Kojima
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplkment au no
8,
Tome 39, aoat 1978, page C6-39FOURTH SOUND HELMHOLTZ RESONATOR I N S U P E R F L U I D ' ~ e T. Chainer, Y. Morii, and H. ~ o j imax
Serin Physics Laboratory, Rutgers University Piscatawzy, New Jersey 08854
R6sum6.- On a utilis6 un rlsonateur de Helmholtz classique pour Gtudier la densitl superfluide dans 1 ' 3 ~ e liquide
.
Abstract.- A classical Helmholtz resonator has been used to study superfluid density of liquide 3 ~ e .
In this paper we describe a measurement of su- perfluid density in liquid 3 ~ e using a Helmholtz resonator. A Helmholtz resonator /I/, a classical acoustic device, consists of a cylindrical open "neck" (cross-sectional area A and length
R)
atta- ched in the wall of a rigid enclosure (volume V). The system can be regarded as a spring (provided by the stiffness of the fluid volume) and a mass(the mass of fluid in the neck). A resonance occurs at a frequency given by
where c is the velocity of sound, and 11 is an ef- fective length /I/. Suppose that the fluid is super- fluid He I1 and that the neck is replaced by a su- perleak in which the normal fluid component is loc- ked. Then it can be shown 121 that eq. (1) conti- nues to hold if c is replaced by the velocity of fourth sound, c+ = (pS/p)'l2 cl where cl is the first sound velocity, p is the superfluid density and p is the total density. If the fluid is super- fluid 3 ~ e , ps should be replaced by anisotropic su- perfluid density ps.'Eq. (1) finally becomes
for fourth sound Helmholtz resonance in superfluid 3 ~ e . A measurement of Helmholtz resonance frequen- cy can be used to determine the superfluid density. A great advantage of the Helmholtz resonance techni-
que is that the frequency can be made significantly lower than conventional fourth sound technique wi- thout a requirement of large size apparatus.
Figure 1 is a schematic diagram of our adia- batic demagnetization cell which incorporates a fourth sound Helmholtz resonator. The cell contains 43 gram of powdered cerium magnesium nitrate (CMN). I
Alfred P. Sloan Foundation Research Fellow
STYCAST 1266 \ELECTRICAL LEAD STAINLESS STEEL
Fig. 1 : Schematic of demagnetization cell.
Temperature is monitored magnetically by 7 mg pow- dered CMN pill using SQUID susceptibility bridge. The volume section (V = 0.413 cm3) of the Helmholtz resonator is fitted with condenser tranducers /3/ with gold plated 6 um Mylar diaphragm as its active element. One transducer acts as a driver and the other as a receiver. The separation between the transducers is 1.00 cm. The neck consists of 20 pa- rallel rectangular channels (only 5 are shown in figure 1) of height equal to 25 um, width 0.569 cm and length 0.305 cm
(A =
2.82 mm2 and II = 0.305 cm) The channels are made by stacking up 0.15 mm thick microscope cover glass separated by brass spacers. To lock the normal fluid component in the neck, the channel height must be less than the viscous pene- tration depth 6 = (rh/pn+£)1'2 wheren
is the vis-n
cosity of norma fluid component (density p n ) . We have cooled 3 ~ e in our cell into superfluid phases at a variety of pressures and have observed fourth sound Helmholtz resonance in both A and B phases. The observed resonance frequency is in rea- sonable agreement with the expected value calcula- ted from eq. (2) using p determined by previous measurements /4,5/. The noise level is at least 40 dB below the signal with 3 Hz band width and the Q of the resonance is 50 at our lowest tempera- ture. In figure 2 we present our data taken in B phase under no applied magnetic field at a pressure of 20.87 bars.
Fig. 2 : Square of Fourth sound Helmholtz resonance frequency versus magnetic temperature.
The square of the Helmholtz resonance frequency, f2, which is proportional to ps/p, is plotted as a function of magnetic temperature T*. At T" = 1.96
.
mK the resonance frequency is 593 Hz. We are able
to follow the resonance to within 10pK of the su- perfluid transition temperature T*. We observe that f2 depends linearly on T* near the transition tem- perature. A critical comparison of our data with previous measurements of p /p cannot be made becau- se the effective length
R
in eq. (2) is not well known. If we take Re = R, then our measurement in figure 2 at T* = 1.96 mK corresponds to p /p =0.047 This value is 19 % smaller than that obtained in reference /4/ at a similar pressure and temperatu- re.We thank Prof. I. Rudnick for useful discus- sions. We would like to acknowledge the assistance of Akhtar Begum in the initial stages of our expe- riment, and the help of Maty Ott in taking and ana-
lyzing data. We acknowledge support by a Research Corporation Grant. This work has been supported by National Science Foundation through DMR 76-82339.
References
/I/ Morse,P.M., Vibration and Sound, McGraw Hill (1 948), New York
/2/ Kriss,M. and Rudnick,I., Phys. Rev.
fi
(1968) 326/3/ Kojima,H., Veith,W., Guyon,E. and Rudnick,I., Journal of Low Temp. Phys.
25
(1976)195 /4/ Kojima,H., Paulson,D.N. and Wheatley,J.C.,Journal of Low Temp. Phys.
