Difference between pulse and periodic waves:
A pulse wave is a sudden disturbance in which only one wave or a few waves are generated, such as in the example of the pebble. Thunder and explosions also create pulse waves. A periodic wave repeats the same oscillation for several cycles, such as in the case of the wave pool, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth periodically through the same positions.
Difference between longitudinal and transverse waves:
A transverse wave propagates when the disturbance is perpendicular to the propagation direction. An example of a transverse wave is where a woman moves a toy spring up and down, generating waves that propagate away from herself in the horizontal direction while disturbing the toy spring in the vertical direction.
In a longitudinal wave, the disturbance is parallel to the propagation direction. Example of longitudinal wave is where the woman now makes a disturbance in the horizontal direction—which is the same direction as the wave propagation—by stretching and then compressing the toy spring.