Additional background on waves:

A wave is a displacement (vibration) that moves through a medium or space. A wave involves some quantity or disturbance that changes in magnitude with respect to time at a given location and changes in magnitude from place to place at a given time. A common example of a wave is circular water waves that are produced by dropping a stone in a calm lake or pond.

A wave cannot exist in only one place, it must move from one place to another. As waves move from place to place they transfer energy not matter.

Only mechanical waves, in addition to an energy source, require a medium to transfer energy. Electromagnetic (light, radio, X-rays) only require an energy source but do not need an elastic medium for transmission of its energy.