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March 30, 2017

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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 - ,

    height= velocity sound*time

  • Physics 203 - ,

    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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