The speed of an airplane is frequently stated in terms of the Mach number, which is simply the ratio between the actual speed and the speed of sound: M = U/a. Suppose an airplane flies at M = 0.8 at...

The speed of an airplane is frequently stated in terms of the Mach number, which is simply the ratio between the actual speed and the speed of sound: M = U/a. Suppose an airplane flies at M = 0.8 at sea level, where the temperature is 27 ◦C; calculate the actual speed of the airplane. Next, calculate the speed at the same Mach number but at an altitude of 13 km, where the temperature is −57 ◦C (for air, γ = 1.4).