A coil spring very popular as a toy (a Slinky) is an easy resource to visualize the three different types of movement in the medium through which a wave passes [1]. First move the end of the spring from side to side, or up and down as in illustration (a) of the figure below. We will observe that a wave of displacement from side to side (or from top to bottom) travels along the quay. Now we push the end of the spring forward and backward, along the direction of the spring itself, as in illustration (b). We now see that a round trip wave travels along the quayside. Finally, we turn the end of the spring rapidly to the right and to the left, as in illustration (c). In this case an angular displacement wave moves along the spring.
A coil spring very popular as a toy (a Slinky) is an easy resource to visualize the three different types of movement in the medium through which a wave passes [1]. First move the end of the spring from side to side, or up and down as in illustration (a) of the figure below. We will observe that a wave of displacement from side to side (or from top to bottom) travels along the quay. Now we push the end of the spring forward and backward, along the direction of the spring itself, as in illustration (b). We now see that a round trip wave travels along the quayside. Finally, we turn the end of the spring rapidly to the right and to the left, as in illustration (c). In this case an angular displacement wave moves along the spring.
The waves like those of (a), in which the displacements are perpendicular to the direction in which the wave travels, are called transverse waves. The waves like those of (b), in which the displacements are in the direction in which the wave travels, are called longitudinal waves. To the waves like those of (c), in which the displacements rotate in a plane perpendicular to the direction of the wave we will call them torsional waves. The three types of wave movement are only found for practical purposes in solids. However, in fluids transverse and torsional waves extinguish very quickly and, in general, can not be produced at all except on the surface. It follows, for example, that the sound waves in the air and in the water are longitudinal. The molecules of the medium move back and forth along the direction in which the sound energy travels [2].
It is usual and very useful to make a graph to represent the patterns of a wave in a medium. Of course, this is very easy to do for transverse waves, but not so much for longitudinal or torsional waves. But there are ways to achieve it. For example, the following graph represents the pattern of compressions at a given time as a sound wave (longitudinal) passes through the air. The graph line goes up and down because the graph represents a snapshot of the increase and decrease in air density and associated pressure along the path of the wave. It does not represent, and this must be emphasized, an up and down movement of the molecules of the air itself.
It is usual and very useful to make a graph to represent the patterns of a wave in a medium. Of course, this is very easy to do for transverse waves, but not so much for longitudinal or torsional waves. But there are ways to achieve it. For example, the following graph represents the pattern of compressions at a given time as a sound wave (longitudinal) passes through the air. The graph line goes up and down because the graph represents a snapshot of the increase and decrease in air density and associated pressure along the path of the wave. It does not represent, and this must be emphasized, an up and down movement of the molecules of the air itself.
To fully describe the transverse waves, such as those of the strings, you must specify the direction of the displacement. When the displacement pattern of a transverse wave is along a line in a plane perpendicular to the direction of wave motion, the wave is said to be polarized. Polarization is usually associated with electromagnetic waves, but it is a phenomenon that affects, in fact, all transverse waves. The following graph shows how polarization is achieved when only one direction of movement is allowed.
These three types of waves (longitudinal, transversal and torsional) have an important feature in common. The disturbances move away from their sources through the medium and continue on their own (although their amplitude may decrease due to the loss of energy due to friction and other causes). We emphasize this specific feature using a specific verb. Thus, we say that the waves propagate. This means more than just saying that they "travel" or "move".
An example will clarify the difference between the waves that propagate and those that do not. You may have seen a wheat field or a meadow of tall grass. When the wind blows ripples occur. The medium for these "waves" is wheat or grass, and the disturbance is the oscillatory movement of each plant. This disturbance actually travels, but does not propagate; that is, the disturbance does not originate from a source and then continues on its own. Unlike the waves we are considering, in the fields of wheat or in the prairies the ripple has to feed continuously by the energy of the wind. When the wind ceases, the disturbance does not continue to move, but also stops. The traveling ripples of the oscillating wheat are not at all the same as waves on a rope or in water. The waves are disturbances that propagate in a medium [1].
Notes:
[1] In the first part of this series we focus on mechanical waves and everything we say, by default, refers exclusively to mechanical waves.
[2] Recall that waves are modes of energy transfer without transfer of matter.