# What is a dispersive and reactive medium in mechanical waves?

Would it be possible to have some explanation about the dispersive and reactive medium in the field of mechanical waves.

As far as I understand :

Let $$\omega$$ be the excitation frequency and $$\omega_0$$ the natural frequency.

• In dispersive medium : sine waves are spread and $$\omega \gt \omega_0$$
• In reactive medium : exponential waves are spread and $$\omega \lt \omega_0$$

However, how can you create them ? For instance, to create a reactive medium, you would add an excitation force (e.g. $$F_0cos(\omega t)$$) at an extremity of the system that would be lower than the lowest mode ? So you would create a lower-pass filter ? I'm not sure to understand how you can create low-pass or high-pass filter.

Last question, I saw that exponential waves are spread without a loss of energy. What does it mean ?