Question

A plane is travelling at Mach 1.50 through air at a temperature of 0 degrees Celsius. If the plane now moves into a cold air mass of -25 degrees Celsius, what will be the cone angle of the sonic boom produced by the plane if it does not change its airspeed?

Answer choices:

a. 72.2 degrees

b. 39.5 degrees

c. 41.8 degrees

d. 44.1 degrees

e. there will not be a cone angle in the higher temperature air mass

Answer 1

Ans

Finding the airspeed of the plane using the Mach number at 0 C

The airspeed v = Mach number * the speed of sound at 0 C

The speed of sound at 0 C = 331 m/s

v = 1.50*331 = 496.5 m/s

So the airspeed of the plane = 496.5 m/s

Now using the following relationship to get the angle of the cone

The speed of sound at - 25 C = 316 m/s

so

So the angle of the cone = 39.5 degrees. Option b is correct.