Kittel's Solid-State Physics: Finding Cutoff Frequency \omega_D

ehrenfest
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Homework Statement


This question refers to Kittel's solid-state physics book.

Above equation (23), Kittel says that a cutoff frequency \omega_D is determined by (19) as" and then he gives equation (23). I have absolutely no idea where equation (23) comes from.


Homework Equations





The Attempt at a Solution

 
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Could you reproduce the equations for those of us who don't have the book handy?
 
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