What is a dispersive and reactive medium in mechanical waves?

[Mathieu]

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 w be the excitation frequency and w0 the natural frequency.

- In dispersive medium : sine waves are spread and w > w0
- In reactive medium : exponential waves are spread and w < w0

However, how can you create them ? For instance, to create a reactive medium, you would add an excitation force (e.g. Fcos(wt)) 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 ?

Edited August 20, 2019 by Mathieu