phy1020.DVI

wherevis the wave speed, the wavelength,dthe ocean depth, andgthe acceleration due to gravity. If
the waves are indeepwater (d>=2), then the hyperbolic tangent in Eq. (9.16) is approximately 1 (i.e.
tanhx 1 for largex), and this reduces to

v

r

g

2

.deep waves;d>=2/: (9.17)

On the other hand, forshallowwaves (d<=20), the hyperbolic tangent in Eq. (9.16) reduces to its argument
(i.e. tanhxxfor smallx), and we have

v

p

gd .shallow waves; d < =20/: (9.18)

Tsunami wavesare waves created by earthquakes. They are unlike normal ocean waves; they have very
long wavelengths (often exceeding 100 km or 60 miles), and they travel at very high speed (typically well
in excess of 500 miles per hour, depending on depth and wavelength) (Eq. (9.16)). The amplitude of a
tsunami wave is very small while the wave is in the deep ocean; a tsunami may pass under a ship without
the passengers even noticing. But when it enters shallow water near shore, a tsunami wave decreases in both
speed and wavelength, resulting in a very destructive wave of very large amplitude.

9.10 Seismic Waves

An example of waves encountered in nature isseismic waves, which are waves in the Earth’s crust and
interior that are produced by earthquakes. Geologists have observed two types of seismic waves that travel in
the interior of the Earth:

• P waves(for “primary” or “pressure” waves) are longitudinal waves, and can travel in both the solid
  and liquid parts of the interior of the Earth.


• S waves(for “secondary” or “shear” waves) are transverse waves, and can travel only in the solid parts
  of the Earth.

The S waves are the slower of the two; they travel at about 60% of the speed of P waves. This is actually why
they are called “primary” and “secondary” waves: the P waves, being faster, arrive first at a seismic observing
station. P waves travel with a speed that varies from less than 5 km/s at the Earth’s crust to about 13 km/s
through the core. From the time delay between the arrival of the P waves and S waves, a seismic observing
station may infer the distance to the earthquake’sepicenter(the point on the Earth’s surface directly above
the point of origin of the earthquake). Measurements from several observing stations allow a determination
of the position of the epicenter through triangulation.
Also, since S waves cannot travel through liquids, observing seismic waves has allowed geologists to
infer something about the structure of the interior of the Earth—for example, that there the core consists of a
solidinner core, surrounded by a liquidouter core.
In addition to P waves and S waves, geologists have observed two types of waves that propagate only at
the surface of the Earth’s crust:Rayleigh wavesripple along the Earth’s surface like water waves, andL waves
(orLove waves) are a kind of transverse wave whose displacement is in the plane of the Earth’s surface.
Seismic wave energy is measured on a logarithmic scale called themoment magnitude scale. An earth-
quake energy ofEjoules is said to have a magnitudeMgiven by

MD^23 log 10 E6:0: (9.19)

For small to medium earthquakes, this moment magnitude scale gives numbers close to those on the older
Richter scale that it replaces.