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The dispersion relation for phonons in a one dimensional monoatomic Bravais lattice with lattice spacing a and consisting of ions of masses M is given by 2c olk)= [1– cos(ka)], where w is the frequency of oscillation, k is the wavevector VM and Cis the spring constant. For the long wavelength modes (2 > a), the ratio of the phase velocity to the group velocity is

The dispersion relation for phonons in a one dimensional monoatomic Bravais lattice with lattice spacing a and consisting of ions of masses M is given by 2c olk)= [1– cos(ka)], where w is the frequency of oscillation, k is the wavevector VM and Cis the spring constant. For the long wavelength modes (2 > a), the ratio of the phase velocity to the group velocity is

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The dispersion relation for phonons in a one dimensional monoatomic Bravais lattice with lattice spacing a and consisting of ions of masses M is given by 2c o(k) = 1- cos(ka), where o is the frequency of oscillation, k is the wavevector M and Cis the spring constant. For the long wavelength modes (2 >> a), the ratio of the phase velocity to the group velocity is
Transcribed Image Text:The dispersion relation for phonons in a one dimensional monoatomic Bravais lattice with lattice spacing a and consisting of ions of masses M is given by 2c o(k) = 1- cos(ka), where o is the frequency of oscillation, k is the wavevector M and Cis the spring constant. For the long wavelength modes (2 >> a), the ratio of the phase velocity to the group velocity is
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