We hear sounds that are carried by sound waves and we see light which is carried by electromagnetic waves. Therefore waves are an important phenomena in our world. In fact at the level of atoms and molecules, waves are much more important than they are in our much larger world. The study of waves and wave phenomena are therefore of fundamental importance to the study of physics. Waves are a manifestation of periodic vibrations of a system.
Vibrations are an every day occurrence in our every day lives.
They occur everywhere in the physical world. A simple pendulum vibrates back and forth with a set period. The string of a violin vibrates back and forth rapidly but still with a set period. The rotation of a wheel can be expressed as the simultaneous simple harmonic motion in both the x and y direction of every part of the rim of the wheel. At the end of one revolution every point has returned to its starting point.