Page:Beat waves.pdf/4

 4. We shall now consider the explicit evaluation of the formula established in $$\S$$3.

Considering the first of the two integrals in equation (9), let the receiver $$R$$ be located on the $$z$$-axis at a height $$z_o$$ (see Fig. 1) and let the path of the projectile be confined to $$xy$$-plane and further be represented by

Finally, let $$P$$ denote the position of the projectile at time $$t$$.



The direction cosines of the instantaneous line of sight $$RP$$ are seen to be

while the direction cosines of the path of the projectile are $$0,\,1,\,0.$$ Accordingly

Hence,