The equation for o(k); the angular frequency for a givenwavenumber of a 1D monatomic crystal is defined as:w(k) =k → k +4K(1)Where K is the spring constant between neighbouring atoms, andm is the mass of each atom.We may note that solutions related by (2) are physicallyequivalent.k2π1 (3)sin2πTaka2(2)Given that the wavenumber in this case is:Where k is the wavenumber of the vibration pattern in terms ofit's wavelength λ- Show that the frequency does not change if (2) is shifted.- Additionally, give your physical reasoning for this occurence.

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Answered: The equation for co(k); the angular…

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The angular frequency of vibrations in a one-dimensional monatomic crystal are given by where w (k) = 4K m sin k = ka 2 2π λ is the wavenumber of the vibration pattern in terms of its wavelength >, the spring constant between neighbouring atoms, and m the mass of each atom. (i) Show that the frequency does not change if one shifts 2π k→ k +. a (ii) Briefly explain the physical reason for this periodicity.
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