Surface waves on fluids with wavelengths in the millimeter range are known as capillary waves. Surface tension determines the propagation and dispersion of capillary waves while gravity plays a minor role. We describe a simple method for generating standing capillary waves of known frequency on water and introduce a novel noncontact technique based on laser interferometry to measure the wavelength of capillary waves with great precision. The data gives the dispersion relation of capillary waves and provides an accurate method for determining the surface tension of fluids.

1.
D.
Langevin
,
Light Scattering by Liquid Surfaces and Complementary Techniques
(
Dekker
,
New York
,
1992
).
2.
J. C.
Earnshaw
, “
Surface light scattering: A methodological review
,”
Appl. Opt.
36
,
7583
7592
(
1997
).
3.
D. M.
Buzza
, “
General theory for capillary waves and surface light scattering
,”
Langmuir
18
,
8418
8435
(
2002
).
4.
R. H.
Katyl
and
U.
Ingard
, “
Line broadening of light scattered from liquid surface
,”
Phys. Rev. Lett.
19
,
64
67
(
1967
).
5.
J. S.
Huang
and
W. W.
Webb
, “
Viscous damping of thermal excitations on the interface of critical fluid mixtures
,”
Phys. Rev. Lett.
23
,
160
163
(
1969
).
6.
K. Y.
Lee
,
T.
Chou
,
D. S.
Chung
, and
E.
Mazur
, “
Capillary wave damping in heterogeneous monolayers
,”
J. Phys. Chem.
97
,
12876
12878
(
1993
).
7.
C.
Martel
and
E.
Knobloch
, “
Damping of nearly inviscid water waves
,”
Phys. Rev. E
56
,
5544
5548
(
1997
).
8.
P.
Cicuta
and
I.
Hopkinson
, “
Dynamic light scattering from colloidal fractal monolayers
,”
Phys. Rev. E
65
,
041404
1
(
2002
).
9.
P.
Cicuta
and
I.
Hopkinson
, “
Recent development of surface light scattering as a tool for optical-rheology of polymer monolayers
,”
Colloids Surf., A
233
,
97
107
(
2004
).
10.
C.
Fradin
,
A.
Braslau
,
D.
Luzet
,
D.
Smilgies
,
M.
Alba
,
N.
Boudet
,
K.
Mecke
, and
J.
Daillant
, “
Reduction in surface energy of liquid interfaces at short length scales
,”
Nature (London)
403
,
871
874
(
2000
).
11.
S.
Hård
,
Y.
Hamnerius
, and
O.
Nilsson
, “
Laser heterodyne apparatus for measurements of liquid surface properties—Theory and experiment
,”
J. Appl. Phys.
47
,
2433
2442
(
1976
).
12.
K. J.
Måløy
,
J.
Feder
, and
T.
Jøssang
, “
An experimental technique for measurement of capillary waves
,”
Rev. Sci. Instrum.
60
,
481
486
(
1989
).
13.
B. J. A.
Bjorkvik
,
D.
Waaler
, and
T.
Sikkeland
, “
A versatile interface light-scattering spectrometer
,”
Meas. Sci. Technol.
6
,
1572
1581
(
1995
).
14.
P.
Tin
,
J. A.
Mann
,
W. V.
Meyer
, and
T. W.
Taylor
, “
Fiber-optics surface light scattering spectrometer
,”
Appl. Opt.
36
,
7601
(
1997
).
15.
T. M.
Jorgensen
, “
A low-cost surface laser light scattering spectrometer
,”
Meas. Sci. Technol.
3
,
26
27
(
1992
).
16.
W. M.
Klipstein
,
J. S.
Radnich
, and
S. K.
Lamoreaux
, “
Thermally excited liquid surface waves and their study through the quasielastic scattering of light
,”
Am. J. Phys.
64
,
758
765
(
1996
).
17.
J.
Lighthill
,
Waves in Fluids
(
Cambridge University Press
,
1978
), p.
208
.
18.
F.
Behroozi
and
N.
Podolefsky
, “
Capillary-gravity waves and the Navier-Stokes equation
,”
Eur. J. Phys.
22
,
587
593
(
2001
).
19.
T. E.
Faber
,
Fluid Dynamics for Physicists
(
Cambridge University Press
,
1995
), p.
174
.
20.
D.
Pnueli
and
C.
Gutfinger
,
Fluid Mechanics
(
Cambridge University Press
,
1992
), pp.
160
162
.
21.
L. D.
Landau
and
E. M.
Lifshitz
,
Fluid Mechanics
, 2nd ed. (
Pergamon
,
New York
,
1987
), p.
245
.
22.
Reference 17, p.
223
.
23.
F. S.
Crawford
, “
A simple model for water-wave dispersion relations
,”
Am. J. Phys.
55
,
171
172
(
1987
).
24.
F. S.
Crawford
, “
Ideal water waves via instantaneous action at a distance
,”
Am. J. Phys.
56
,
300
303
(
1988
).
25.
F. S.
Crawford
, “
Speed of gravity waves in deep water: Another elementary derivation
,”
Am. J. Phys.
60
,
751
752
(
1992
).
26.
H.
Georgi
,
The Physics of Waves
(
Prentice Hall
,
Englewood Cliffs, NJ
,
1993
), pp.
294
297
.
27.
F.
Behroozi
and
N.
Podolefsky
, “
Dispersion of capillary-gravity waves: a derivation based on conservation of energy
,”
Eur. J. Phys.
22
,
225
231
(
2001
).
28.
F.
Behroozi
,
B.
Lambert
, and
B.
Buhrow
, “
Direct measurement of the attenuation of capillary waves by laser interferometry: Non-contact determination of viscosity
,”
Appl. Phys. Lett.
78
,
2399
2402
(
2001
).
29.
F.
Behroozi
,
B.
Lambert
, and
B.
Buhrow
, “
Noninvasive measurement of viscosity from damping of capillary waves
,”
ISA Trans.
42
,
3
8
(
2003
).
30.
F.
Behroozi
, U.S. Patent No. 6,563,588 B2: “
Apparatus and method for measurement of fluid viscosity
” (13 May
2003
).
31.
F.
Behroozi
and
P. S.
Behroozi
, “
Efficient deconvolution of noisy periodic interference signals
,”
J. Opt. Soc. Am. A
23
,
902
905
(
2006
).
32.
K. S.
Birdi
,
Lipid and Biopolymer Monolayers at Liquid Interfaces
(
Plenum
,
New York
,
1989
), pp.
32
37
.
33.
A. W.
Adamson
,
Physical Chemistry of Surfaces
, 5th ed. (
Wiley
,
New York
,
1990
), pp.
4
45
.
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