A wave can indeed travel through a non-elastic medium. The ability of a wave to propagate in a medium depends on the medium's physical properties, rather than its elasticity.
Elasticity refers to a material's ability to deform under stress and return to its original shape when the stress is removed. Elastic materials, like a spring, can undergo deformation and then restore their original shape once the applied force is removed.
However, the propagation of a wave through a medium is determined by the medium's ability to transmit energy and disturbances. This property is governed by factors such as the density, compressibility, and intermolecular forces within the medium.
In non-elastic mediums, such as fluids (liquids and gases), the particles are not bound in a fixed arrangement like in a solid. When a wave passes through a fluid, the particles can move and rearrange themselves, allowing the wave to propagate. This is evident in the case of sound waves, which can travel through air or water, both of which are non-elastic mediums.
It's important to note that the speed and behavior of waves in different mediums can vary significantly. Elastic materials, such as solids, often transmit waves more efficiently due to their tightly bound particles, while non-elastic mediums may introduce more damping or attenuation to the wave as energy is dissipated in the form of heat or other forms of energy.