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?
height= velocity sound*time
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.
To find the plane's altitude, we will use the formula:
Altitude = (Speed of Sound × Time Delay) / 2
Given that the speed of sound is 340 m/s and the time delay is 20 s, we can substitute these values into the formula:
Altitude = (340 m/s × 20 s) / 2
Altitude = (6800 m) / 2
Altitude = 3400 m
Therefore, the plane's altitude is 3400 meters.