If a plane is flying at a speed so that the apex half-angle of its shockwave is 30 $\degree$, what is its speed if the speed of sound is 320 m/s?
A)960 m/s
B)640 m/s
C)320 m/s
D)160 m/s
E)Choose this answer if a shock wave cannot form in this situation.

Question

Quizplus · Accepted Answer

The formula for finding the speed of a plane generating a shock wave with a given apex half-angle is:
v = M × a, where v is the speed of the plane, M is the Mach number, and a is the speed of sound.
The half-angle of the shockwave can be used to find the Mach angle using the formula:
sin(Mach angle) = 1/M
Thus, sin(30°) = 1/M, which gives M = 2
Therefore, v = 2 × 320 m/s = 640 m/s, which is answer choice B.

If a Plane Is Flying at a Speed So That °\degree°

If a Plane Is Flying at a Speed So That $\degree$