The angular frequency of vibrations in a one-dimensional monatomic crystal are given by where w(k) = 4K m sin k = ka 2 2π X 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.
The angular frequency of vibrations in a one-dimensional monatomic crystal are given by where w(k) = 4K m sin k = ka 2 2π X 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.
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb360a251-a88e-4e24-b6e1-ceeebc35a45e%2Ff009b62c-da7f-451a-a838-81fbb8df0c7a%2Fwvg1dfj.jpeg&w=3840&q=75)
Transcribed Image Text: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.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)