3.5 Visualisation of a Wave Using SciLab
21
its argument by 2π (the Greek symbol “pi”), where π is about 3.1415. Accordingly,
we can express a wave travelling in the x-direction as:
A(x, t) = A o sin
2π
x
λ
−
t
T
(3.2)
where A is a property experiencing oscillations such as sea level, A o is the constant
wave amplitude, being half the difference between maximum and minimum values
of A, λ is wavelength, and T is wave period. This wave displays sinusoidal variations both in time and space. Equation (3.2) describes a wave void of variation in the
y direction. Accordingly, wavefronts (crests and troughs) are parallel to each other.
A wave like this is called a plane wave.
3.5 Visualisation of a Wave Using SciLab
3.5.1 A Simple Wave Made of Vertically Moving Bars
In order to visualise a wave, we consider a number of vertical bars sitting in a row
next to each other. Bars rise or sink in a systematic pattern. The firs bar gives the
rhythm by moving up and down in a sinusoidal fashion. Any neighboring bar does
the same but slightly delayed in time. Whenever a bar is above a certain horizon, it
turns blue. When it is below this horizon, it turns red.
Figure 3.3 shows a snapshot of this wave. There is no lateral motion of any of the
bars, but the pattern seems to move toward the right. The speed at which the pattern
moves is called phase speed of a wave.
3.5.2 Sample Script
The SciLab script for this wave demonstration, called “WaveSim.sce”, can be found
in the folder “Miscellaneous” on the CD-ROM of this book. Before using this script,
however, the reader should read the following brief introduction to SciLab scripting.
Fig. 3.3 Snapshot of organised wave motions by bars
21
its argument by 2π (the Greek symbol “pi”), where π is about 3.1415. Accordingly,
we can express a wave travelling in the x-direction as:
A(x, t) = A o sin
2π
x
λ
−
t
T
(3.2)
where A is a property experiencing oscillations such as sea level, A o is the constant
wave amplitude, being half the difference between maximum and minimum values
of A, λ is wavelength, and T is wave period. This wave displays sinusoidal variations both in time and space. Equation (3.2) describes a wave void of variation in the
y direction. Accordingly, wavefronts (crests and troughs) are parallel to each other.
A wave like this is called a plane wave.
3.5 Visualisation of a Wave Using SciLab
3.5.1 A Simple Wave Made of Vertically Moving Bars
In order to visualise a wave, we consider a number of vertical bars sitting in a row
next to each other. Bars rise or sink in a systematic pattern. The firs bar gives the
rhythm by moving up and down in a sinusoidal fashion. Any neighboring bar does
the same but slightly delayed in time. Whenever a bar is above a certain horizon, it
turns blue. When it is below this horizon, it turns red.
Figure 3.3 shows a snapshot of this wave. There is no lateral motion of any of the
bars, but the pattern seems to move toward the right. The speed at which the pattern
moves is called phase speed of a wave.
3.5.2 Sample Script
The SciLab script for this wave demonstration, called “WaveSim.sce”, can be found
in the folder “Miscellaneous” on the CD-ROM of this book. Before using this script,
however, the reader should read the following brief introduction to SciLab scripting.
Fig. 3.3 Snapshot of organised wave motions by bars