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 ?