Pulse Wave:
A pulse wave is a non-repeating wave. It is a single disturbance.
Periodic Wave:
A periodic wave requires regularly repeating disturbances. It is a wave that occurs at a regular interval.
Transverse Wave:
This wave is caused by us pulling the spring sideways at a right angle to the way in which the wave will travel.
Longitudinal Wave:
A longitudinal wave is when a disturbance occurs in the same direction of travel. It is caused by several turns of the spring being compressed and then let go.