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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/cm3; at 20 degrees C and
standard atmospheric pressure, the surface tension of the water/air
interface is 73 gm/sec2. 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 vphase =
2vgroup = (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; confusing the two can cause serious
misunderstandings. 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"!
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