Differentiate between transverse and longitudinal waves.

Transverse waves vibrate perpendicular to the direction of propagation, while longitudinal waves vibrate parallel to the direction of propagation.

Transverse waves are characterised by the movement of the medium (the material through which the wave is travelling) in a direction perpendicular to the direction of energy transport. This means that the particles of the medium are moving in a direction that is up and down (or left and right), while the energy of the wave is moving forward. Examples of transverse waves include light waves, radio waves, and the ripples on the surface of water when a stone is thrown into it.

On the other hand, longitudinal waves are characterised by the movement of the medium in a direction parallel to the direction of energy transport. This means that the particles of the medium are moving back and forth along the same direction that the wave is moving. Examples of longitudinal waves include sound waves and seismic P-waves (primary waves that are part of an earthquake).

The difference in the movement of the medium in transverse and longitudinal waves also leads to differences in their wave diagrams. A transverse wave diagram shows crests and troughs, which represent the maximum displacement of the medium in the positive and negative directions respectively. A longitudinal wave diagram, however, shows compressions and rarefactions, which represent regions where the medium is compressed and stretched respectively.

In terms of polarisation, only transverse waves can be polarised. Polarisation is a property of waves that describes the orientation of their oscillations. For transverse waves, this can be vertical, horizontal, or at any angle in between. However, for longitudinal waves, polarisation is not applicable as the oscillations are along the direction of wave propagation.

In summary, the key difference between transverse and longitudinal waves lies in the direction of vibration relative to the direction of wave propagation. This difference leads to other distinguishing characteristics such as the ability to be polarised for transverse waves and the representation of wave diagrams.