Waves dissipate energy when they propagate through real medium. Theoretical study of waves is one of important way to understand the nature of waves in medium with dissipation. The study points out that the theoretical solution to the wave equation describing a disturbance propagating in a dissipative medium is not unique, which is determined by the dissipation mechanism of the medium. A new general solution is proposed by assuming that the attenuations of disturbance can occur in the time and space domains. The general solution is further used in case studies. The properties of viscoelastic waves propagating in the Kelvin-Voigt medium and electromagnetic waves propagating in conductive medium with the reciprocal attenuation in time and space domains are analyzed. The result shows that the attenuation mechanism has an obvious influence on the properties of waves in the dissipative medium when the wave equations are the same.
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