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JulijaS [17]
3 years ago
14

The phase velocity of transverse waves in a crystal of atomic separation a is given byy = csin(ka/2) pka/2 1. What is the disper

sion relation e(k)? 2. What is the group velocity as a function of k?
Physics
1 answer:
damaskus [11]3 years ago
7 0

Answer:

a

e(k) =  \frac{2a}{c}  *  sin (\frac{k*a}{2} )

b

G_{v} =  \frac{d e(k ) }{dk }  =  \frac{a^2}{c}  *  cos (\frac{k* a}{2} )

Explanation:

From the question we are told that

    The  velocity  of transverse waves in a crystal of atomic separation is  

                  b_y  = c \frac{sin (\frac{k*a}{2} )}{\frac{k*a}{2} }

Generally the dispersion relation is mathematically represented as

            e(k) =  b_y  *  k

=>    e(k) = c  \frac{sin(\frac{k*a}{2} ) }{ \frac{k*a}{2} }  *  k

=>    e(k) =   c *  \frac{sin (\frac{k_a}{2} )}{ \frac{a}{2} }

=>    e(k) =  \frac{2a}{c}  *  sin (\frac{k*a}{2} )

Generally the group velocity is mathematically represented as

          G_{v} =  \frac{d e(k ) }{dk }  =  \frac{a^2}{c}  *  cos (\frac{k* a}{2} )

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