What a Surface Wave Is
A surface wave is a wave that occurs at the interface between
different media (material layers) and is localized to that
interface. Typically, the amplitude of the surface wave decreases
exponentially with increasing distance from the interface. The rates
exponential decrease in the two media will generally differ.
Sometimes the amplitude of the surface wave in one of the media
is zero. For example, with sound waves at an interface between
solid and a vacuum, the sound wave obviously does not penetrate into
the vacuum. In such cases, the amplitude of the surface wave will
still decrease exponentially in the other medium.
Some examples of Surface waves
The most commonly seen surface waves are water waves.
The amplitude of gravity waves  on the surface of water
falls off as
e-d/L, where L is the wavelength and d is the
below the surface.  So water waves atop a body of water
deeper than their wavelength are surface waves.  Tsunamis, on the
other hand, have a wavelength that is large compared to the depth of the ocean,
Suppose you have an interface between a vacuum and an ideal
elastic solid which is isotropic and homogeneous.
 A kind of surface wave called Rayleigh
waves can occur there.  If the elastic solid is covered
with a thin layer in which s-waves travel more slowly than in the
medium below, there a kind of transverse wave called Love waves can
occur.  Love waves are often called surface waves although
they require this additional layer to occur. Love waves and Rayleigh
waves can be considered to be sound waves.
Earthquake waves are sound waves in the earth , and
Rayleigh waves and Love waves are the two types of earthquake waves that
travel along the surface of the earth.
Surface acoustic wave (SAW) devices use sound waves at the surface
of piezoelectric materials. Many of them use
Rayleigh waves; however there are a variety of other waves that can
occur at the surface of an electromagnetic medium, and some use those.
The most common kind of SAW device is a low power filter for
signals at microwave or radio frequencies. A cell phone might have as many as four of these SAW filters.
Surface plasmons, sometimes called "surface plasmon-polaritions",
electromagnetic surface waves. The ground
in radio is mathematically the same as a surface
References, Notes, and Random Pedantry
- What I am calling “gravity waves” are not the gravitational waves
predicted by general relativity. Suppose you have one or more fluids
in a gravitational field with density decreasing as you go upwards. If you
disturb the fluid(s) from hydrostatic equilibrium you can get oscillations. The restoring force on a piece of fluid comes from the
difference between the buoyancy force on it and its weight and is vertical.
These oscillations are often called gravity waves.
- “Waves. Berkeley Physics Course - Volume
3.”, by Frank S. Crawford (McGraw-Hill Book Company, New
York, 1968) gives a pretty complete derivation for gentle water waves
of small amplitude in section 7.3, except that it ignores viscosity.
- Some books say that water waves are transverse.
They are wrong. In a water wave, a piece of fluid moves in an ellipse. The
ellipse lies in the plane that contains both the vertical and the direction
in which the wave is moving.
- In case you have trouble picking out the correct definitions, a
homogeneous if it is the same everywhere. This of course can’t be true
atomic scale but it can be true on larger scales. If a solid is
direction in the solid acts the same as any other direction in the
- “A treatise on the mathematical theory of elasticity”, by A.E.H.
Love, 4th edition (Dover Publications, New York, 1944)
which is a reprint of a 1927 edition by Cambridge Press. Article 214
discusses Rayleigh waves.
- “Some problems of geodynamics; being an essay to which the Adams
prize in the University of Cambridge was adjudged in 1911”, by A.E.H. Love
(Dover Publications, New York, 1967), which is a reprint of the 1911 edition
by Cambridge Press, chapter XI, especially sections 176 through 181.
- In most places the earth is neither homogeneous nor isotropic, nor
yet is it perfectly elastic, but it is
close enough for solutions derived for homogeneous isotropic solids to
- Ground waves in radio are sometimes called Zenneck waves.