Do sound dissipation depend on the medium it travels on or its frequency?
Yes to both. As sound is a mechanical wave (rather than an electromagnetic one), the more effective the dissipative mechanisms of the medium, the more dissipation the wave will experience. Dissipation due to viscosity is a good mechanism. Expect an acoustic wave traveling through honey to dissipate more quickly than the same wave traveling through water. Frequency dependence: consider the dynamics of the Fourier transform of the dissipation equation (this also shows why more viscosity leads to more dissipation.) u_t = nu u_xx U_t = -k^2 nu U; where k is the Fourier wave number, nu is the viscosity and U is the Fourier coefficient associated with the wave number k. Solving for U, you find exponential decay of the amplitude of U. So decay is faster when (k is large) and when (nu is large). Large k is associated with waves having high frequency — so dissipation affects high frequency waves more effectively (be least resistant to dissipation.) Large nu is associated with very viscous medi
