Back to Topic 4

Graphical Representation of Waves

We can show that both longitudinal and transverse waves can be represented by a displacement-distance graph.  If we take a snapshot of a wave at any instant, we see:

For a transverse wave we see that the graph looks very similar to the actual wave.

For a longitudinal wave the graph is not so easy to see.

Let us look at the air molecules in their undisturbed positions and compare them as a sound wave passes by.

If we plot displacement on the y-axis and distance on the x-axis, we get the same graph to what we had before.   The shape is a sine wave.

If we plot a displacement-time graph for a single particle we see:

This is true whether we have a longitudinal or transverse wave.  If we connect a microphone to a CRO, the CRO displays a displacement-time trace.  It is important that we do not confuse the displacement-distance with the displacement-time graph. The latter tells us nothing of the wavelength, only the period (hence the frequency) of the wave.

The simplest shape of graph we see is the sine wave.  The sine wave equation links wave motion with simple harmonic motion.   Sine waves in sound are very boring to listen to.  The quality of the sound gives us important clues as to the source.  Sounds made by different musical instruments have very different wave patterns, even if the notes sounded and the volumes are the same.

How much do you know about Transverse and Longitudinal Waves?  Click HERE

Polarisation of Transverse Waves

Polarisation is a feature of transverse waves only.  Longitudinal waves are never polarised. We say that a wave is plane polarised if all the vibrations in the wave are in a single plane, which contains the direction of propagation of the wave.  Suppose we have a rope and make waves down it.  We could make waves in any direction we liked.  But if we made waves through a narrow vertical slit, we would find that the waves would only pass through if they were vertical. This would be a vertically polarised wave.

Light waves are easily polarised using polaroid filters.  Light waves, like all electromagnetic waves, consist of an electric field component perpendicular to a magnetic field component, which are always in phase.  We normally consider only the electric field component in polarisation, because the electrical effects are those that dominate.  The unpolarised waves are normally oriented in any direction.

If two polaroid filters are mounted such that they are parallel, the light will pass through both the first at which point it is vertically polarised, and then through the second.

If the two filters are crossed, so that the transmission planes are at 90^o to each other, the vertically polarised light gets blocked, because it cannot pass the horizontal transmission plane. No light passes.

Crossed polaroids are found in liquid crystal displays on calculators and petrol pumps.