A Wave Perspective
Katsushika
Hokusai created his enduring image of `The Great Wave` around
1832. The inscription translates to ‘Under a Wave off Kanagawa`
and depicts two boats struggling against the power of a great wave with
Mount Fuji in the background. However, while Hokusai’s image is the
more beautiful illustration of the power or energy of a wave, we need
to turn to science to better explain the underlying nature of waves.
Therefore, we will start by providing some sort of definition of a mechanical
wave, which is the class of wave associated with a physical medium like
water:
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A mechanical wave travels through a medium by means of a `mechanical` interaction between adjacent or neighbouring particles within that medium. |
However, we should clarify from the start that a wave is a mechanism that transports energy independent of matter. As such, there is no wholesale movement of the particles in the medium, although mechanical waves do depend on these particles `vibrating` in some manner, such that the energy of the wave can be transferred. Therefore, we might generalised the previous definition of a wave to:
A wave is a mechanism that transports energy `independent` of matter
This definition is subject to certain caveats that will be highlighted in a number of examples as we progress the discussion of mechanical waves. However, while it is not the subject of this section, we should possibly make some reference to electromagnetic waves travelling through a vacuum. In the case of an electromagnetic wave, the energy transfer is considered totally independent of any mechanical interactions between neighbouring particles. Therefore, these waves are subject to a different description and, for this reason, the discussion of electromagnetic waves is deferred until after we have established some of the basic principles associated with mechanical waves. The discussion of mechanical waves will be sub-divided into 3 broad sections.
- Introduction of waves in 1, 2 and 3 dimensions
- The basic physics of simple harmonic motion (SHM).
- The nature of waves in terms of superposition, harmonics, energy & velocity.
In an attempt to help the visualisation of some of these concepts, a number of programs have been written to help produce a number of animated GIFs. However, given the general level of discussion, the programming details behind these animations will not be expanded within the description itself.