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Shock Wave Cone Problem

  1. Apr 9, 2008 #1
    1. The problem statement, all variables and given/known data
    You look directly overhead and see a plane exactly 1.4·km above the ground, flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.4·km.

    (a) Find the angle of the shock wave cone.

    (b) Find the speed of the plane (Mach number).


    2. Relevant equations
    Sin (shock wave cone angle)=(c/v)

    PLane Speed= v/c

    v=velocity of source

    c=speed of sound

    3. The attempt at a solution
    The plane is 1400 meters high. When the shockwave is heard, the plane has travelled 2400 meters horizontally. Sound travels at 343 m/s. 1400/343 gives me 4.08 seconds. 2400/4.08 gives the plane a speed of 588 m/s.

    Sin-1(343/588)=35.7 degrees. Of course, I'm here because these are not the correct answers and I don't know why. Any clues as to what I did wrong would be greatly appreciated.
     
  2. jcsd
  3. Apr 12, 2008 #2

    tiny-tim

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    Hi negatifzeo! :smile:

    You're not thinking clearly. :frown:

    The sound leaves the plane before it's overhead.

    Draw a diagram. There's a right-angled triangle in it. You know one of the angles has sin c/v (which one?). Then use Pythagoras' theorem! :smile:
     
  4. Apr 12, 2008 #3
    I don't understand. It makes sense that the planr makes a sound before its directly overhead, of course. But how can you solve for sin c/v without knowing the aircraft's speed?
     
  5. Apr 12, 2008 #4

    tiny-tim

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    Because v is an unknown, just like x in ordinary algebra equations.

    Draw the diagram … use v, or a multiple of v, where you would normally use a number … and you'll get an equation in v (maybe linear, maybe quadratic) … which you can then solve.

    Try it (and start with the diagram)! :smile:
     
  6. Jun 23, 2008 #5
    I'm having problems with this question too.

    I understand that the angle is Tan-1 (1.4/2.4) = 30.25 degrees

    But how do you go about finding the mach number? I also calculated teh speed as 588 m/s, making the Mach speed 1.78, but that wasn't right.
     
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