Posted by **Mike** on Tuesday, May 11, 2010 at 2:20am.

A supersonic plane flies directly over you at 1.8 times the sound speed. You hear its sonic boom 20s later.

What is the plane's altitude, assuming a constant 340 sound speed?

- Physics 203 -
**bobpursley**, Tuesday, May 11, 2010 at 6:32am
height= velocity sound*time

- Physics 203 -
**drwls**, Tuesday, May 11, 2010 at 8:49am
The angle that the bow shock wave makes with the velocity vector, and with the ground, is

A = sin^-1 (1/M) = 33.8 degrees.

The relationship between altitude h and sonic boom delay time t is:

h/(Vt) = tan A = 0.668

where V = airplane speed = M*Vsound = 612 m/s

Thus

h = 0.668 v t = 818 m

BobPursley's formula would result in

680 m.

The shock wave cone behind the airplane moves faster than the speed of sound.

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