Show that the equation of motion of identical atoms of mass M in a chain, M dt2 d²Un = K (Un+1 + Un-1 – 2Un) , ecomes the continuum elastic wave equation, with vs as the sound velocity for the long wavelengths, a²U dx?

icon
Related questions
Question
Show that the equation of motion of identical atoms of mass M in a chain,
K (Un+1+ Un-1 –- 2Un) ,
dt2
becomes the continuum elastic wave equation, with vs as the sound velocity for the long wavelengths,
1 0²U
Transcribed Image Text:Show that the equation of motion of identical atoms of mass M in a chain, K (Un+1+ Un-1 –- 2Un) , dt2 becomes the continuum elastic wave equation, with vs as the sound velocity for the long wavelengths, 1 0²U
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer