Why do waves move faster at higher temperatures and in a solid phase?

there is more energy and the particles are farther apart.
there is less energy and the particles are closer together.
there is less energy and the particles are farther apart.
there is more energy and the particles are closer together.

Correct answer is:

There is more energy and the particles are closer together.

In fact, waves are essentially vibrations of the particles of the medium they are travelling through. In solids, particles are closer together, therefore there is less distance between them and vibrations can be transmitted faster, so waves can travel faster. Moreover, at high temperatures particles move faster (because they have greater kinetic energy), so they are more energetic and collisions happen more efficiently, therefore vibrations are transmitted faster and waves can travel faster as well.

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