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 dispersion relation e(k)? 2. What is the group velocity as a function of k?

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  

Generally the dispersion relation is mathematically represented as

=>    

=>    

=>    

Generally the group velocity is mathematically represented as

answer

procedural programming, object-oriented programming

explanation

procedural programming is a type of computer programming language that specifies a series of well structured steps and procedures   within its development period of time. it contains a systematic order of statements, functions and commands to complete a computational task or program. it is centered on creating procedures. while object oriented programming is a programming language that is centered on creating objects rather that actions and data rather than logic.. it has four principles which are inheritance, polymorphism, abstraction and encapsulation

prndulum needs thread, weight clock to time swings