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?
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d1fc48-d7b2-428e-9847-83620ea7fe5b%2Fc018bd2c-102c-460d-aecc-3c58ff86b0cf%2F775fq8y_processed.jpeg&w=3840&q=75)
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