Physics for Geologists, Second edition

8 Basic concepts
all the relevant dimensions must be scaled in the right proportion, and if
we wish to scale a process that takes millions of years so that we can see
its effect in days, we use material in the model that is much more fluid,
such as wax. See Hubbert (1937) for a better understanding of the the-
ory of scale models, and Ramberg (1981) for interesting applications to
geology.
Speed, velocity and acceleration
As you drive through a town, your speedometer tells you your speed [LT-l]
over the ground. This is variable and, knowing the distance travelled and
the time taken to travel it, your average speed can be calculated. Your route
will probably not have been straight, so that progress towards your goal has
been slower than your progress over the road. Velocity is the net speed in
a particular direction. It is a vector: it has magnitude and direction. Speed
is a scalar: it has magnitude but no direction. A yacht tacking to windward
may be travelling at 6 knots through the water, but its velocity to windward
will be about 614 4 knots. If a current is flowing, the velocity over the
sea floor will be different again. Writers (including this one) are not always
consistent in making this distinction, but the context usually makes it clear.
Acceleration [LT-2] is the rate at which speed or velocity changes with
time. It has direction and magnitude and is therefore a vector. Acceleration
in physics is not necessarily in the direction of motion, or opposed to it. It is
in the direction of the force applied, which causes the acceleration. A football
kicked in the air has a downward acceleration due to gravity that gives it
its trajectory. The component of velocity parallel to the ground would be
constant if there were no air resistance.
Frequency, wavelength, amplitude and phase
As waves come into the coast, the distance between them - the wavelength,
X - is fairly constant but becomes shorter as the beach is approached;
the height of the wave from trough to crest (or amplitude, which is half the
height of the wave) is fairly constant, but becomes greater as the beach is
approached; and the frequency (symbol v, the Greek letter nu) or period
(112, or T) with which the waves break on the beach remains fairly constant.
The speed or velocity (c) of waves is variable and a function of wavelength.
The dimensions of frequency are T-l; of wavelength, L. So the relationship
between velocity [LT-'1, wavelength and frequency is Tpl = LT-'/L; in
words, frequency times wavelength gives velocity or, X = clv.
Waves are additive (Figure 1.1), so if two parallel wave trains are in the
same phase (that is, their crests and troughs coincide) much bigger waves
and deeper troughs will result. If they are exactly opposite in phase, small
lumpy waves will result. If the wave trains are not identical, not parallel,
more complicated interference will be seen.
Copyright 2002 by Richard E. Chapman