We consider elastic waves in isotropic and anisotropic media and discuss their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. The waves are represented by a wave function. For isotropic media this representation greatly simplifies the theory. The reflection of quasitransverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles.

1.
L. D.
Landau
and
E. M.
Lifshitz
,
Theory of Elasticity
(
Reed Educational and Professional Publishing
,
Oxford
,
1999
).
2.
P. M.
Morse
and
H.
Feshbach
,
Methods of Theoretical Physics
(
McGraw-Hill
,
New York
,
1953
), Part 1.
3.
E.
Dieulesaint
and
D.
Royer
,
Ondes Élastiques dans les Solides
(
Masson
,
Paris
,
1974
).
4.
R.
Truell
,
C.
Elbaum
, and
B. B.
Chick
,
Ultrasonic Methods in Solid State Physics
(
Academic
,
New York
,
1969
).
5.
J. P.
Musgrave
,
Crystal Acoustics
(
Holden-Day
,
San Francisco
,
1970
).
6.
F. I.
Fedorov
,
Theory of Elastic Waves in Crystals
(
Plenum
,
New York
,
1968
).
7.
A. N.
Nikitin
,
T. I.
Ivankina
, and
V. K.
Ignatovich
, “
The wave field patterns of the propagation of longitudinal and transverse elastic waves in grain-oriented rocks
,”
Izvestiya, Physics of the Solid Earth
45
,
424
436
(
2009
).
8.
W. P.
Leung
, “
Demonstration of shear waves, Lamb waves and Rayleigh waves by mode conversion
,”
Am. J. Phys.
48
,
639
642
(
1980
).
9.
The reflected and refracted wave fields contain the waves of three different modes, which propagate at different angles and with different speeds. Some of these modes become surface waves and specular reflection is absent.
10.
V. K.
Ignatovich
, “
On neutron surface waves
,”
Crystallogr. Rep.
54
,
116
121
(
2009
).
11.
A. P.
Kiselev
, “
Energy flux of elastic waves
,”
J. Sov. Math.
19
,
1372
1375
(
1982
).
12.
I. A.
Victorov
,
Sound Surface Waves in Solids
(
Nauka
,
Moscow
,
1981
) (in Russian).
13.
S. K.
Tomar
, “
Propagation of Stoneley waves at an interface between two microstretch elastic half-spaces
,”
J. Vib. Control
12
,
995
1009
(
2006
).
14.
K. A.
Ingerbrigtsen
and
A.
Tonning
, “
Elastic surface waves in crystals
,”
Phys. Rev.
184
,
942
951
(
1969
).
15.
D. F.
Parker
, in
Surface Waves in Anisotropic and Laminated Bodies and Defects Detection
, edited by
R. V.
Goldstein
and
G. A.
Maugin
(
Kluwer Academic
,
Dordrecht
,
2004
).
16.
“Seismic waves,” Wikipedia, ⟨en.wikipedia.org/wiki/Seismic_wave⟩.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.