The topic of 8.981 will be *gravitational waves*. Contrary to
some material floating out there, the topic will **not** be gravity
waves. Since some people might have an interest in "gravity waves,"
here is a brief description:

"Gravity waves" (commonly referred to as "water waves") are modes excited in an incompressible fluid. One source of restoring force is provided by gravity (hence "gravity waves"); a second is provided by surface tension. The dispersion relation of these waves is given by

where *k* is the wavenumber, *rho* is the fluid density,
*sigma* is the fluid's surface tension, and *h* is the
water's depth.

For water, *rho* = 1 gm/cm^{3}; at 20 degrees C and
standard atmospheric pressure, the surface tension of the water/air
interface is 73 gm/sec^{2}. The gravity and surface tension
terms are thus roughly equal at a wavelength of about 1.7 cm; the
gravity term dominates for longer wavelengths. This is the regime of
"gravity waves" proper.

In deep water, *kh* >> 1; the hyperbolic tangent limits to 1, and
the dispersion relation becomes

The phase and group velocities are given by v_{phase} =
2v_{group} = (*g/k*)^{½}. Note that long
wavelength modes have higher group velocity than short wavelength
modes.

In shallow water, *kh* << 1, it usually suffices to take the
first two terms in the expansion of the hyperbolic tangent:

In very shallow water, the second term can be neglected and the waves are non dispersive.

This discussion was adapted from the text *Vibrations and waves in
physics*, by Iain G. Main.

It's worth emphasizing that being super careful with this nomenclature is not just anal retentive; it can in fact be very confusing to confuse the two. For example, "gravity waves" of the type discussed here can occur in the fluid that constitutes a neutron star. In such a circumstance, you can actually have "gravitational waves" arising from "gravity waves"!