Answer to Question #102620 in Classical Mechanics for BIVEK SAH

Question

Explain how a linear monoatomic chain behaves as a low pass filter

Answer 1

In the simplest crystal of mono-atomic chain, in which atoms are connected in the one dimensional identical atoms. The chain consists the very large number of identical atoms which connected to each other and that connection is act as the spring.

Let the stiffness of the spring is k and the mass of the atom is m, frequency will be $\omega_o=2\sqrt{\dfrac{k}{m}}$

In this oscillations, the atoms can oscillate only in one direction.So the chain will behave like low pass filter, so that the wave can propagate without the attenuation. The waves decays continuously that is called the evanescent waves