Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit
We report the results of experiments to explore interactions between physically separated oscillating objects in isotopically pure superfluid ⁴He at T ∼ 10 mK. The investigations focused mainly on 32 kHz quartz tuning forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidt...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Cite this: | Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit / D. Garg, V.B. Efimov, M. Giltrow, P.V.E. McClintock, L. Skrbek // Физика низких температур. — 2012. — Т. 38, № 11. — С. 1300–1305. — Бібліогр.: 31 назв. — англ. |
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irk-123456789-1179212017-05-28T03:04:05Z Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit Garg, D. Efimov, V.B. Giltrow, M. McClintock, P.V.E. Skrbek, L. К 75-летию Л.П. Межова-Деглина We report the results of experiments to explore interactions between physically separated oscillating objects in isotopically pure superfluid ⁴He at T ∼ 10 mK. The investigations focused mainly on 32 kHz quartz tuning forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidth (LDL) and resonant frequency fd of a detector fork were monitored while the maximum velocity of a transmitter fork, separated from the detector by a few mm, was varied over a wide range. Clear evidence was found for mutual interactions between the two forks, and for the influence of the grid on the forks. Monitoring the detector's LDL and fd provides evidence for a generator critical velocity in the range 0.3 < vc₁ <1.0 cm/s for onset of the detector responses, in addition to a second critical velocity vc₂ ∼ 13 cm/s probably corresponding to the production of quantum turbulence at the generator. The results are discussed, but are not yet fully understood. 2012 Article Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit / D. Garg, V.B. Efimov, M. Giltrow, P.V.E. McClintock, L. Skrbek // Физика низких температур. — 2012. — Т. 38, № 11. — С. 1300–1305. — Бібліогр.: 31 назв. — англ. 0132-6414 PACS: 67.25.dk, 47.27.Сn http://dspace.nbuv.gov.ua/handle/123456789/117921 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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К 75-летию Л.П. Межова-Деглина К 75-летию Л.П. Межова-Деглина |
| spellingShingle |
К 75-летию Л.П. Межова-Деглина К 75-летию Л.П. Межова-Деглина Garg, D. Efimov, V.B. Giltrow, M. McClintock, P.V.E. Skrbek, L. Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit Физика низких температур |
| description |
We report the results of experiments to explore interactions between physically separated oscillating objects
in isotopically pure superfluid ⁴He at T ∼ 10 mK. The investigations focused mainly on 32 kHz quartz tuning
forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidth (LDL) and resonant frequency
fd of a detector fork were monitored while the maximum velocity of a transmitter fork, separated from the detector
by a few mm, was varied over a wide range. Clear evidence was found for mutual interactions between the
two forks, and for the influence of the grid on the forks. Monitoring the detector's LDL and fd provides evidence
for a generator critical velocity in the range 0.3 < vc₁ <1.0 cm/s for onset of the detector responses, in addition to
a second critical velocity vc₂ ∼ 13 cm/s probably corresponding to the production of quantum turbulence at the
generator. The results are discussed, but are not yet fully understood. |
| format |
Article |
| author |
Garg, D. Efimov, V.B. Giltrow, M. McClintock, P.V.E. Skrbek, L. |
| author_facet |
Garg, D. Efimov, V.B. Giltrow, M. McClintock, P.V.E. Skrbek, L. |
| author_sort |
Garg, D. |
| title |
Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit |
| title_short |
Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit |
| title_full |
Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit |
| title_fullStr |
Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit |
| title_full_unstemmed |
Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit |
| title_sort |
mutual interactions between objects oscillating in isotopically pure superfluid ⁴he in the t → 0 limit |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2012 |
| topic_facet |
К 75-летию Л.П. Межова-Деглина |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117921 |
| citation_txt |
Mutual interactions between objects oscillating in isotopically pure superfluid ⁴He in the T → 0 limit / D. Garg, V.B. Efimov, M. Giltrow, P.V.E. McClintock, L. Skrbek // Физика низких температур. — 2012. — Т. 38, № 11. — С. 1300–1305. — Бібліогр.: 31 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
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| first_indexed |
2025-07-08T13:01:20Z |
| last_indexed |
2025-07-08T13:01:20Z |
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1837083847025491968 |
| fulltext |
© D. Garg, V.B. Efimov, M. Giltrow, P.V.E. McClintock, and L. Skrbek, 2012
Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 11, pp. 1300–1305
Mutual interactions between objects oscillating in
isotopically pure superfluid 4He in the T → 0 limit
D. Garg1, V.B. Efimov1,2, M. Giltrow1, P.V.E. McClintock1, and L. Skrbek3
1Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
2Institute of Solid State Physics RAS, Chernogolovka 142432, Moscow Region, Russia
E-mail: efimov@issp.ac.ru
3Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Prague 121 16, Czech Republic
Received June 13, 2012
We report the results of experiments to explore interactions between physically separated oscillating objects
in isotopically pure superfluid 4He at T ∼ 10 mK. The investigations focused mainly on 32 kHz quartz tuning
forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidth (LDL) and resonant frequency
fd of a detector fork were monitored while the maximum velocity of a transmitter fork, separated from the detec-
tor by a few mm, was varied over a wide range. Clear evidence was found for mutual interactions between the
two forks, and for the influence of the grid on the forks. Monitoring the detector's LDL and fd provides evidence
for a generator critical velocity in the range 0.3 < vc1 <1.0 cm/s for onset of the detector responses, in addition to
a second critical velocity vc2 ∼ 13 cm/s probably corresponding to the production of quantum turbulence at the
generator. The results are discussed, but are not yet fully understood.
PACS: 67.25.dk Vortices and turbulence;
47.27.Сn Transition to turbulence.
Keywords: superfluid helium, tuning fork, oscillating grid, quantum turbulence, acoustic resonance.
In Celebration of Professor Leonid P. Mezhov-Deglin’s 75th Birthday
1. Introduction
First, we are much indebted to the Editorial Board of
Low Temperature Physics for their invitation to contribute
to this special issue marking the 75th birthday of Professor
Leonid P. Mezhov-Deglin, whose seminal and imaginative
contributions to low temperature physics still continue af-
ter spanning more than half a century.
In what follows, we describe an extension of a recent
investigation [1] of individual quartz tuning forks oscillat-
ing in isotopically pure superfluid 4He near 10 mK. We
report the results of experiments to measure the mutual
interactions between pairs of forks, and to study the influ-
ence on individual forks of quantum turbulence (QT) being
generated by a nearby oscillating grid.
Quantum turbulence is currently being investigated
through studies of the resonant dynamics of a variety of
different objects oscillating in both He II and 3He–B, at-
tracting considerable attention and interest. Examples of
such objects include spheres [2–4], wires [5–10] and grids
[11–13]. Quartz tuning fork resonators [14–16] are the
latest sensors to join this family of vibrating objects. They
are quite small (∼ mm), and therefore convenient for use at
low temperatures. They have been used as thermometers,
viscometers and pressure sensors [15] in all the helium
fluids, as well as in QT studies in He II. Forks have been
shown [15,17–21] to generate QT over a wide range of
temperatures. The question naturally arises, therefore, as to
whether forks can also act as detectors of vortex lines? In
He II at relatively high temperatures, > 1.3T K, attempts
to answer this question suggest that the detection is at best
inefficient: a standard 32 kHz fork has been shown to
detect a submerged counterflow jet [22], but only if its
velocity exceeds about 20 cm/s, and attempts to detect
even a rather high vortex line density generated at 1.3 K
between counterrotating discs seem not to have been suc-
cessful [20]. It has been shown, however, that free vortex
rings from a fine vibrating wire can trigger the transition to
turbulence in the initially vortex-free boundary flow
around another vibrating wire at ∼ 30 mK [23].
Mutual interactions between objects oscillating in isotopically pure superfluid 4He in the T → 0 limit
Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 11 1301
Although superfluid 4He in its low-T limit is much like
a vacuum, or æther, interactions between a pair of objects
can occur through the creation of excitations that pass from
one to the other. In addition to quantized vortices, there
may be individual phonons travelling ballistically, or
waves of first sound made up of large numbers of coherent
phonons; second sound does not exist at these temperatures
because there is no normal fluid component per se. Rotons
are unlikely to be created on account of the relatively large
velocities needed [24–26]. So in seeking explanations for
any interactions that are observed between uncharged os-
cillators in the absence of magnetic fields, the only me-
chanisms needing to be considered are probably those in-
volving either phonons/sound or vortices/QT.
Quantum turbulence is created in the superfluid by an
oscillating object when it exceeds a critical velocity 2c ∼v
∼ 10 cm·s 1− . There is also evidence for a lower critical
velocity 1c ∼v 0.1–0.9 cm·s–1 at which there are changes
in flow that can lead to increased dissipation. The underly-
ing mechanism is unknown, but some possibilities are dis-
cussed in [1].
It has recently become apparent that emission of sound
from forks can provide an important source of energy loss
[1,27,28], leading to their low-drive-linewidths (LDLs)
being much larger than in a vacuum. Calculations [1] have
shown that the dissipation at low drives can be attributed to
coupling of the oscillatory modes of the fork to acoustic
modes of the experimental cell containing the helium sam-
ple, considered as a resonant cavity. For a relatively large
cell, as used in our present experiments, the acoustic mod-
es are very closely-spaced. Consequently, tiny changes in
the velocity of sound, corresponding to very small pressure
variations in the cell, can bring them into or out of reson-
ance with the fork, resulting in corresponding variations in
the LDL.
2. Experimental techniques
The experiment was performed in a 3He–4He dilution
refrigerator at its base temperature of ∼ 10 mK. The large
experimental cell, holding ∼ 1.5 of isotopically pure 4He
under a pressure of 5 bar, was described earlier in connec-
tion with vibrating grid experiments [13,29,30]. The ar-
rangement of the forks and grid in the cell is described in
[1]. Briefly, one fork (f1) was on the cylindrical axis of the
cell, 1 mm above the grid. The other one (f2) was mounted
10 mm above f1. The forks oscillated in planes parallel
with the grid, but were mounted with an angle of 120° be-
tween their axes of symmetry. A third fork positioned out-
side the electrode structure (f3) was not in line-of-sight of
the grid or other forks. Forks f1 and f2 were bare, with their
encapsulating cans completely removed; the can of f3 was
left in place, but it was opened by removal of its top to
allow access by the superfluid helium.
The filling tubes to the cell descended through the main
4He bath at 4.2 K, and were closed off by valves at the top
of the cryostat. As the level of helium gradually fell in the
bath, the pressure rose by about 0.02 bar, causing the ve-
locity of sound to increase by about 4 parts in 104 which
(see Sec. 1) was sufficient to cause one or more acoustic
modes to pass through resonance with the fork oscillations.
Consequently, although results are highly reproducible
over a few tens of minutes, measurements of the LDL or
resonant frequency on longer timescales were typically
characterised by slow oscillatory drifts. The latter must be
borne in mind thoughout the rest of the paper but, because
we are mostly looking for responses to changes, they do
not in general have a large influence on the interpretation
of the results.
3. Experimental results
To seek evidence of inter-fork interactions, we operated
f1 as a detector and f2 as a generator. In what follows, the
numbers given for both the generator and detector responses
corresponds to the maximum prong velocity in each case.
Fig. 1. Response of the detector fork f1 to switching on the exci-
tation of the generator f2. The low-drive linewidth dfΔ (a) and
frequency f (b) are plotted as functions of time for the generator
velocities indicated by the numbers (in mVRMS) beside the traces.
The generator is switched on at = 100t s, and off at = 200t s.
The detector velocity was 0.3 mm/s, i.e.,
1
< .cv v
1.2
1.0
0.8
0.4
0 100 200 300
D
et
ec
to
r
L
D
L
,
H
z
0.6
200
100
60
40
30
20
10
0.9, 2
(a)
Time, s
(b)
0.9
2
100
20
30 40
60
10
200
D
et
ec
to
r
fr
eq
u
en
cy
,
H
z
f
32102.4
32102.3
32102.2
Time, s
0 100 200 300
D. Garg, V.B. Efimov, M. Giltrow, P.V.E. McClintock, and L. Skrbek
1302 Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 11
Calculations of the prong velocity, and of the force on the
fork due to the excitation, were based on the relationships
given by Blaauwgeers et al. [15]. In our experiments at
10T ∼ mK a slow change in the behaviour of the fork re-
sponse max ( )F F∝v began at a velocity max 1∼v cm/s
[1]. A transition to QT generation by the fork began at the
the much higher velocity of 15∼ cm/s, where it manifested
as a dependence 2
max ( ) .F F∝v The detector was conti-
nuously driven at a low level ( ∼v 0.3 mm/s), and its LDL
and resonant frequency were monitored. Figure 1 shows
how the detector responds when the generator is driven on
resonance for periods of 100 s, each successive period cor-
responding to an increased generator drive. For generator
velocities that are less than a certain value, probably corres-
ponding to 1cv (see Sec. 1), there is almost no effect. At
higher generator velocities the LDL of the detector increases
linearly (not illustrated), and the detector frequency falls,
until the generator velocity reaches a critical value probably
corresponding to 2 .cv Above this second critical velocity
the LDL of the detector continues to increase, albeit at a
slower rate, while the detector frequency starts to increase
again. In some experiments the detector response was more
complicated. For example, the change of behaviour of the
LDL on exceeding 2cv may manifest either as an increasing
LDL or to a decreasing LDL, as we discuss below.
We have also conducted experiments in which the de-
tector LDL and resonant frequency were tracked conti-
nuously, but where the velocity of the generator was stea-
dily and slowly ramped up and then down, without
switching it off, with results as shown in Fig. 2(a)–(c). It is
clear that the detector LDL (b) does not start to change
noticeably until the generator velocity (a) has attained a
value that is of order 1c ∼v 1 cm/s, whereupon it increases
rapidly until the generator velocity has reached a value of
order 2c ∼v 13 cm/s, after which it starts decreasing
again. The behavior is nicely mirrored as the generator
velocity ramps down again. A similar measurement con-
ducted with a much higher detector velocity (∼ 40 cm/s,
within the turbulent regime) showed only a negligible de-
tector response to the generator.
We note that the results shown in Figs. 1 and 2(a)–(c)
are qualitatively different, in that the detector LDL in-
creases monotonically with increasing generator drive in
the former case, while in the latter case the detector LDL
falls when the generator velocity exceeds 2 .cv This differ-
ence seems not to be due to the different experimental pro-
cedure, but rather to a non-reproducibility of the detector
response. This is confirmed in the data of Fig. 3 where, in
effect, the measurements of Fig. 2 were repeated four times
at intervals during a 4-hour period. The results at about
14:50, for example, were rather similar to those of Fig. 2;
in those near 13:15 the LDL variation was opposite in sign,
but the positive monotonic change in resonant frequency
was similar to that seen in Fig. 2(b). If the roles of the de-
tector and the generator forks were exchanged, qualitative-
ly very similar behaviour was observed. Comparable inte-
ractions with f3 could also be detected but were much
weaker.
Evidence was found for the influence of the grid on
forks f1 and f2, but there was no measurable influence of
either fork on the grid. Figure 4 illustrates the changes in
the LDL and resonant frequency of f1 while the amplitude
of the driving force on the grid is slowly ramped up and
then ramped down again. The velocity of the grid, plotted
in (a) is flat-topped on account of QT production once 2v
has been exceeded. Panels (b) and (c) show clear evidence
for almost discontinuous changes in fΔ and f when the
grid velocity is near 2 ,v but they are extremely small.
Fig. 2. Generator f2 velocity and corresponding detector f1 res-
ponses while the generator drive amplitude is swept continuously
up and then down again. Resultant generator velocity (a). Reso-
nant width (b) and resonant frequency of the detector (c). The
detector velocity was 0.3 mm/s, i.e.,
1
< .cv v
L
D
L
,
H
z
10
1.0
0.1
1.4
1.2
1.0
0.8
32102.2
32101.8
(a)
(b)
(c)
vc2
vc1
19:32 19:36 19:40 19:44 19:48 19:52
Time, hrs:mins
G
en
er
at
o
r
v
el
o
ci
ty
,
cm
/s
f,
H
z
L
D
L
,
H
z
Fig. 3. Four episodes in which the generator f2 drive amplitude is
swept continuously up and then down again, much as in Fig. 2. Re-
sultant generator velocity (a), resonant width (b) and resonant fre-
quency of the detector f1 (c). The detector velocity was 0.3 mm/s,
i.e.,
1
< .cv v The corresponding generator LDLs are shown by the
numbers adjacent to the responses.
(a)
(b)
(c)
10
1.0
0.1
0.01
1.0
0.8
0.6
0.4
31619.6
31619.4
31619.2
f,
H
z
G
en
er
at
o
r
v
el
o
ci
ty
,
cm
/s
L
D
L
,
H
z
13:00 14:00 15:00 16:00 17:00
Time, hrs:mins
1.40
0.49
0.43
0.47
Mutual interactions between objects oscillating in isotopically pure superfluid 4He in the T → 0 limit
Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 11 1303
Note that the “tilt” on both plots is attributable to the tiny
pressure changes discussed in Sec. 2.
Figure 5 illustrates the influence of the grid on f2, over
a longer interval: in effect, it shows 4 repeats of Fig. 4, but
using f2, and with the grid quiescent for most of the time.
As shown in (a) the grid velocity is swept up and down
slowly, 4 times. The resultant changes in fΔ and f are
plotted in (b) and (c), respectively. Nearly discontinuous
changes occur in both quantities, superimposed on slowly
drifting backgrounds. Of particular note is the fact that the
changes in fΔ and f in response to the grid being ener-
gised can be either positive or negative.
4. Discussion and conclusions
It is clearly evident from the experimental results that the
forks and grid affect each other, but that their mutual influ-
ence is complex. We emphasize that the coupling definitely
occurs via the superfluid: the detector does not respond to
the generator in vacuum, and nor does it do so in He I. The
resonant frequencies (32.102 kHz and 31.615 kHz for forks
f2 and f1, respectively) are sufficiently far apart that the pos-
sibility of electrical cross-talk can be ignored, as can also a
possible resonant response of the detector to mechanical
vibrations of the generator. The same is true a fortiori for a
fork and the grid. The fork velocities are many orders of
magnitude below those needed for direct roton or phonon
generation.
As mentioned above, acoustic coupling of the forks to
cavity modes is always important, and the slow time-
variations can be attributed to this effect, but it is not clear
whether or how it would affect inter-fork coupling. The
onset of communication near the generator 1cv and the
sudden change in behaviour at its 2cv would not be ex-
pected for a gradually increasing acoustic field. So it seems
likely that quantized vortices are involved, especially in the
latter case.
The results of Fig. 2 show that the onset of the increase
in LDL occurs at 1,c∼ v and the subsequent sudden de-
crease in LDL occurs at 2 .c∼ v Figure 5 shows, however,
that the response of the detector fork can be exactly oppo-
site in sign: the initial interaction as the generator velocity
increases can be either positive or negative, but still with a
sign-reversal above the second critical velocity. These var-
iations in the sign of the detector response, as exemplified
in Figs. 3 and 5, are puzzling. It seems, however that, at
least for the relatively small number of data recorded, the
detector LDL at the time of the measurement may be sig-
nificant. In Fig. 3(b), for example, the sign of the LDL
changes depends on whether the initial LDL is above or
below 0.5 Hz. For lower LDL, the initial response at 1c∼ v
is always negative, but the LDL starts to increase again at
2 .c∼ v For initial LDLs above 0.5 Hz, exactly the opposite
behavior is seen. In the case of the LDL in grid-fork inte-
ractions (Fig. 5(b)) the initial response is negative if the
initial LDL is above 0.36 Hz, and positive if the initial
LDL is below this width. The frequency changes asso-
ciated with fork-fork or grid-fork interactions do not seem
to depend on the initial LDL in any consistent way.
It seems implausible that the grid could produce signifi-
cant acoustic effects, given its relatively low resonant fre-
quency of / 2ω π∼ 1 kHz and the fact that acoustic emis-
sion from a dipolar source of this kind should be
proportional to 4.ω The well-established acoustic effects
for forks, on the other hand, are consistent with their high-
er frequency (here 32 kHz) and the fact that, as quadrupole
sources, their emission should vary as 6ω as discussed in
detail by Bradley et al. [31]. It is evident from Fig. 4 that,
Fig. 4. Observation of grid-to-fork influence, showing the grid
velocity and corresponding detector responses while the grid
drive amplitude is swept continuously up and then down again.
The detector velocity was 0.3 mm/s, i.e.,
1
< .cv v Resultant grid
velocity (a), resonant width (b) and resonant frequency of the
detector fork f1 (c).
f,
H
z
10
1
0.46
0.44
32103.46
32103.44
22:00 22:10 22:20 22:30
Time, hrs:mins
G
ri
d
v
el
o
ci
ty
,
m
m
/s (a)
(b)
(c)
Generator – HV grid
Detector – bottom fork
Fig. 5. Four episodes in which the grid drive amplitude is swept
continuously up and then down again, much as in Fig. 4; in be-
tween these episodes the grid was undriven. Grid velocity, (a),
resonant width (b) and resonant frequency of the detector fork f2
(c). The detector velocity was 0.3 mm/s, i.e.,
1
< .cv v
10
1
0.44
0.36
0.28
m
m
/s
G
ri
d
v
el
o
ci
ty
,
31620.22
31620.18
f,
H
z
15:00 18:00 21:00
Time, hrs:mins
(c)
(b)
(a)
Generator – HV grid
Detector – top fork
D. Garg, V.B. Efimov, M. Giltrow, P.V.E. McClintock, and L. Skrbek
1304 Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 11
consistent with the earlier work at higher temperatures
[20,22], the influence of QT on a fork is very weak. It also
appears oddly discontinuous. The onset of the change in
fΔ is very sudden, but then it hardly alters although the
QT density is increasing very substantially as the driving
force on the grid is ramped towards its maximum. In com-
mon with the fork-fork interactions, the grid-fork interac-
tion can be either positive or negative (Fig. 5).
Although we have no detailed understanding of the me-
chanism underlying the sign changes in the responses, it
seems very likely to be associated with acoustics, perhaps
in combination with vortices. Tiny changes in the frequen-
cy mismatch between the fork and an acoustic mode can
result in drastic changes in the response (see Fig. 8 of [1]).
One may speculate, for example, that the impinging vortic-
es will always tend to load the fork thereby reducing its
frequency. Depending on whether the fork frequency is
just above or just below the nearest acoustic mode of the
cell, the coupling of the fork to the acoustic mode could be
either increased or reduced, with a corresponding increase
or reduction in ;fΔ in addition, one might expect the pres-
ence of vortices to have some direct influence in increasing
.fΔ Yet another possible effect to be borne in mind could
involve QT shielding the detector fork from a flux of vor-
tex rings from the fork generator when operated in the high
velocity range. Which of these effects is dominant could
depend on the separation in frequency of the fork oscilla-
tion from the acoustic mode.
In summary, therefore, we can conclude that in “free
space” within the æther of superfluid 4He in its low teme-
rature limit:
— Tuning forks exhibit measurable interactions, proba-
bly attributable to quantized vortices but complicated by
the couplings between the forks and acoustic modes of the
cell. In particular, we observed marked changes in the de-
tector response characteristics as the generator velocity
passed through the velocity 1cv and exceeded the critical
velocity 2 .cv
— A tuning fork can detect the oscillations of a near-
by grid, probably by being affected by the QT it is gene-
rating — but it is relatively insensitive as a QT detector.
— For both fork-fork and grid-fork interactions, the re-
sponse can be of either sign; but there are indications that
the magnitude of the initial detector LDL may be what
determines the sign of the LDL changes observed as the
generator power is changed.
Further work will be needed to arrive at a detailed un-
derstanding of the phenomena discussed above, in particu-
lar to try to separate the acoustic and vortex-influenced
effects, perhaps through use of a cell with walls or internal
components designed to maximise acoustic absorption.
We gratefully acknowledge many valuable discussions
with W.F. Vinen. The investigations were supported by the
Engineering and Physical Sciences Research Council (UK)
and the Russian Academy of Sciences programme “Quan-
tum mesoscopic disordered systems”.
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