An airplane is warming up its engine on the ground. The intensity of sound energy U (dimension M L'1 T'Z) from the propeller at a distance d ahead of the airplane depends in addition to d on the diameter D of the propeller, the rotational speed a) (dimension T'l) of the propeller, the mass density p (dimension M L'3) of air, the air pressure p (dimension M L'1 T\"), and the air viscosity u (dimension M L'1 T"). a) Use dimensional analysis to identify four nondimensional numbers: the nondimensional intensity of sound energy U* that is proportional to U, the nondimensional distance d* that is proportional to d, the nondimensional rotational speed toy, that is proportional to 03, and the nondimensional viscosity pi: that is proportional to 14. Use the exponents of U, (1, c0, and u as independent parameters to nd these numbers. Write these numbers by using the velocity scale vp = (p / p)\