Transverse and Longitudinal Waves 1

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Transverse waves are easy to draw; longitudinal waves are difficult to draw.

The mathematics of wave motion easily maps into diagrams for transverse waves, but it does not map so easily into diagrams for longitudinal waves.

So, transverse wave diagrams end up being easier to work with when studying this material.

However, the world is filled with examples of both types of waves. So, how does one easily represent longitudinal waves?

Basically, both transverse and longitudinal waves share the same mathematical structures and formulas. So, one must learn to transfer the meaning from a transverse wave diagram into the meaning of a longitudinal wave diagram. This can be done by carefully examining the above animation.

Notice that the crest of a transverse wave can move along with the compression of the longitudinal wave. Notice that the trough can move along with the rarefaction.

Therefore, the crest in a transverse wave diagram can represent the compression in a longitudinal wave. A similar representation exists between the trough and the rarefaction.

So, a transverse wave drawing can be interpreted to represent a longitudinal wave.

One need not map the crest into the compression and the trough into the rarefaction. One could map the crest into the rarefaction and the trough into the compression. In fact, one could map the slope of the transverse diagram into the longitudinal diagram. For example, the location of the steepest positive slope on the transverse diagram could be matched with the compression on the longitudinal diagram, and the location of the steepest negative slope could be matched with the rarefaction on the longitudinal diagram.

Usually, though, we will think of it as the crest representing the compression, the trough the rarefaction.

Therefore, transverse wave diagrams can be used to represent the behavior and mathematics of longitudinal waves.

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