Question

Evaluate the proprgation velcocity of acoustic vibrations in aluminum whose Debye temperature id `Theta= 396K`.

Answer 1

We apply the same formula but assume `v_(||) ~~ v_(_|_)`. Then
`Theta=( ħ)/(k)v(6pi^(2)n_(0))^(1//3)`
or `v=kTheta//[ ħ(6pi^(2)n_(0))^(1//3)]`
For Al
`n_(0)=(rhoN_(A))/(M)= 6.023xx10^(22) per c.c`
Thus `v=3.39km//s.`
The tabulated values are `v_(||)= 6.3km//s`
and `v_(_|_)= 3.1km//s`