The best explanation is the <em>difference</em> between the inside <em>temperature</em> and the outside temperature.
If the player doesn't change his emboucher (muscles and position of his lips), then the pitch produced by the instrument depends only on the physical dimensions of its plumbing, and the speed of sound in the tube.
BOTH of those things change slightly when the temperature changes.
Answer:
a
e(k) = \frac{2a}{c} * sin (\frac{k*a}{2} )
b
G_{v} = \frac{d e(k ) }{dk } = \frac{a^2}{c} * cos (\frac{k* a}{2} )
Explanation:
From the question we are told that
The velocity of transverse waves in a crystal of atomic separation is

Generally the dispersion relation is mathematically represented as

=> 
=> 
=> 
Generally the group velocity is mathematically represented as

Imagine a car crash. A car coming at a high speed has a head on collision with a car at rest. When the car makes impact, it will move the other car with it at a slower speed then it was travelling at. In this case, the velocity decreased since the car slowed down, but the mass increased since there are now two cars moving. Momentum was conserved because the change in mass accounts for the loss of velocity.
Your answer should be D
let me know if I got it wrong
Hope this helped!