A wave may be described as a disturbance that travels through a medium from one location to another.
A wave transmits energy from one place to another.
For example: energy can be carried by a water wave generated by a boat out at sea, or by a sound wave from a loudspeaker to a listener’s ear.
A wave can be observed on a slinky with one end fixed and the other end allowed to be altered.
In its natural, unstretched state, a slinky assumes an equilibrium/rest position with all the coils evenly spaced. If the first coil on the free end is displaced, the remaining coils are also displaced, and if stretched and released, a disturbance is produced which can be observed moving through the slinky from one end to the other.
If the slinky is given a simple back and forth vibration, the observed motion of the disturbance is called a pulse.
A pulse may be defined as a single disturbance, moving through a medium from one location to another.
If the coil, however, continuously and periodically vibrates back and forth, a repeating disturbance moving with the slinky is observed over a prolonged period.
This periodic, repeating disturbance which moves through the coil is called a wave.
A wave is a periodic disturbance which travels through a medium from one location to another.
A medium is a substance or material which carries or transports the disturbance, i.e. the wave. The wave medium (similar to a news medium, which carries news from one location to another) transports the wave from one location to another.
The wave medium is not the wave, and it does not create the wave; it simply transports it from its source to some other location. In the case of the slinky, the medium is the slinky coils. The water in the ocean is the medium through which a water wave travels, whereas a sound wave usually travels through air.