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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 ?

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