The angle at the vertex of the cone-shaped shock wave produced by a plane breaking the sound barrier is related to the Mach number M describing the plane's speed by the equation 1/sin θ/2 = M. For what value of cos θ will the Mach number be 2?

Question

Please explain/show work!

2951 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-15T06:47:26

#1/sin(theta/2)=M#

Given #M=2#

So #1/sin(theta/2)=2#

#=>sin(theta/2)=1/2=sin30^@#

#=>theta=60^@#

Hence #costheta=cos60^@=1/2#