The medium of a wave is the substance or material that transports or carries the wave from its source to another location. For example, in a water wave, the water is the medium which carries the wave. It is however important to note that the medium of a wave is not the wave and doesn't make up the wave. Each is entirely different from the other.
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Medium wave, commonly abbreviated as MW is the component of the medium frequency, FM radio band used primarily for AM broadcasting. It has been in use since the beginning of 1920's by radio stations to serve a confined or regional audience.
A medium in waves refers to the platform through which mechanical waves vibrate. Some of the common mediums on which waves travel through include water (water waves) and air (sound waves). Waves travel fastest in air and slowest in solids.