A large amount of energy E is suddenly released in the air as in a point of explosion. Experimental evidence suggests that the radius r of the high-pressure blast wave depends on time t as well as the energy E and ρ the density of the ambient air.
a. Using the Buckingham method, find the equation for r as a function of t, ρ, and E.
b. Show that the speed of the wave front decreases as r increases.