A large amount of energy E is suddenly released in the air as in a point of explosion. Experimental evidence suggests the radius r of the high-pressure blast wave depends on time t as well as the...

A large amount of energy E is suddenly released in the air as in a point of explosion. Experimental evidence suggests the radius r of the high-pressure blast wave depends on time t as well as the energy E and r the density
of the ambient air.

(a) Using the Buckingham method, find the equation for r as a function of t,
, and E.

(b) Show that the speed of the wave front decreases as r increases.