Question

If the speed of sound is 340 m/s a plane flying at 400 m/s creates a conical shock wave with an

apex half angle of:
​

Answer 1

The apex half angle of the conical shock wave created by the plane is approximately 49.0 degrees.

Step-by-step explanation:

To find the apex half angle of the conical shock wave created by the plane, we can use the formula for the Mach angle. The Mach angle (θ) is the angle between the direction of the moving object (plane) and the edges of the shock wave cone. It is given by:

θ = sin^(-1)(1 / Mach number)

where the Mach number (M) is the ratio of the plane's speed to the speed of sound:

M = Plane Speed / Speed of Sound

Given that the speed of sound is 340 m/s and the plane is flying at 400 m/s, we can calculate the Mach number:

M = 400 m/s / 340 m/s ≈ 1.17647

Now, we can find the Mach angle (θ):

θ = sin^(-1)(1 / 1.17647) ≈ 49.0 degrees

So, the apex half angle of the conical shock wave created by the plane is approximately 49.0 degrees.