(a) In connection with Eq. (7.35b), explain why

is the tiny volume occupied by a collection of the wave’s quanta.

(b) Choose for the collection of quanta those that occupy a cross sectional area A orthogonal to a chosen ray, and a longitudinal length △s along the ray, so V = A△s. Show that d ln △s/dt = d ln C/dt and correspondingly,

(c) Given part (b), show that the conservation law (7.35b) is equivalent to the constancy of nCA along a ray, Eq. (7.35c).

(d) From the results of part (c), derive the constancy of

along a ray(where A is the wave’s amplitude), Eq. (7.35d)

Equations

V.Vgd In V/dt, where V