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Answer» Actually it depends on the type of waves
for eg TRANSVERSE and longitudinal waves
In transverse waves the direction of propagation of wave is perpendicular to the direction of motion of string and it TRAVELS in vacuum not require and MEDIUM because they consist of oscillating electric (E) and magnetic (B) fields which are perpendicular. eg em waves and light whereas in longitudinal waves displacement of the particle is along the direction of wave and it requires a medium for propagation for eg sound waves it represents longitudinal waves because they consist of rarefaction and compression which are propagating in the wave.
*medium can be solid or LIQUID or GAS which also depends on their intermolecular forces between the molecules.
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