rumus matematika

3.1. Draw the profile for k = 1, 2, and 5 / 2 . Explain why
L is called the wavelength of the wave (profile).
For a tsunami, and other waves, the surface elevation
is usually zero outside a bounded interval. As an
example of such a ‘confined’ wave, we introduce just
one wiggle of the sine-function, and give it for this
lesson a temporary name Single Sine and notation:
( )
sin ( ) for 0 2
Sin
0 else
x x
x
≤ ≤ π
=
⎧⎨⎩
3.2. Draw this function and, on the same axis, also the
functions Sin (x+1), Sin(x+4π).
Box 3: Simplest description of waves: the dynamics
As said, a dynamic description of waves requires us to
specify the surface elevation at each instant. If we
denote the time by t , we get a function of both time
and space: η =η(x,t). In the simplest case, the wave
profile just translates with a fixed speed. For instance,
consider the dynamics of our Single Sine wave given
by
(1) η ( x,t)=aSin(kx−ωt)
At t = 0 , we recognize the wave profile with amplitude
a .
At a specific position, say at x = 0 , this function
describes the surface elevation at that position as
function of time,
η (0,t)=aSin(−ωt).
Here, ω (omega, the Greek letter ‘w’) is called the
(angular) frequency, and T =2π /ω is the (time) period
of the wave.
3.3. Draw η (0, t ) as function of time.
3.4. Show that c= ω /k is the speed of the wave.
3.5. Show that we can also write c=L/T.
This is part I of two course letters that deal with various aspects of waves on the surface of water. In this partI we
mainly deal with the most dramatic type of waves, the tsunami waves. In part II we