The equation for co(k); the angular frequency for a given wavenumber of a 1D monatomic crystal is defined as: 4K ka w(k) = √√|sin (47). (1²). 2 (1) Where is the spring constant between neighbouring atoms, and m is the mass of each atom. We may note that solutions related by (2) are physically equivalent. k→ k + k 2π Given that the wavenumber in this case is: 2πT (2) (3) Where k is the wavenumber of the vibration pattern in terms of it's wavelength > - Show that the frequency does not change if (2) is shifted. - Additionally, give your physical reasoning for this occurence.
The equation for co(k); the angular frequency for a given wavenumber of a 1D monatomic crystal is defined as: 4K ka w(k) = √√|sin (47). (1²). 2 (1) Where is the spring constant between neighbouring atoms, and m is the mass of each atom. We may note that solutions related by (2) are physically equivalent. k→ k + k 2π Given that the wavenumber in this case is: 2πT (2) (3) Where k is the wavenumber of the vibration pattern in terms of it's wavelength > - Show that the frequency does not change if (2) is shifted. - Additionally, give your physical reasoning for this occurence.
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Transcribed Image Text:The equation for o(k); the angular frequency for a given
wavenumber of a 1D monatomic crystal is defined as:
w(k) =
k → k +
4K
(1)
Where K is the spring constant between neighbouring atoms, and
m is the mass of each atom.
We may note that solutions related by (2) are physically
equivalent.
k
2π
1 (3)
sin
2πT
a
ka
2
(2)
Given that the wavenumber in this case is:
Where k is the wavenumber of the vibration pattern in terms of
it'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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