An airplane flying faster than the speed of sound of 340 m/s produces a shock wave that makes an angle of 50° with the direction the plane is flying.What is the speed of the plane?
A) 490 m/s
B) 530 m/s
C) 390 m/s
D) 440 m/s
E) 405 m/s

Question

Quizplus · Accepted Answer

The angle of the shock wave (θ) can be related to the Mach angle (μ) by the equation:

θ = arcsin(1/μ)

We are given that θ = 50° and the speed of sound is 340 m/s. Solving for μ, we get:

μ = 1/sin(50°) = 1.292

The speed of the plane (v) can then be found using the equation:

v = μ × speed of sound = 1.292 × 340 m/s ≈ 439.8 m/s ≈ 440 m/s

Therefore, the best choice is D.

An Airplane Flying Faster Than the Speed of Sound of 340