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Another sound question

  1. Jun 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A jet aircraft travelling with a velocity of mach 1.5 at an altitude of 5029m passes directly over an observer on the ground. How many seconds elapse before the observer experiences the sonic boom created by the jet? speed of sound= 343ms-1


    2. Relevant equations



    3. The attempt at a solution
    the only example i can find of this in my book has only this equation (its for the angle of the shock cone) sin theta = v sound/ v object. Can anyone give me any help on how i can work out the time from this, im pretty sure you have to use this equation at some point. Can anyone give any help please.
     
  2. jcsd
  3. Jun 17, 2008 #2

    Dick

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    Draw a picture. The sound will reach you when the shock cone hits you. It's a trig problem. Work out the horizontal distance the plane needs to travel for that. Then use that to find the time.
     
  4. Jun 17, 2008 #3
    i did that an got the angle as 0.8867. then i used tan-1 x adjacent equals opposite, which i had as the horizontal distance. Then i used time = distance/velocity but still get the wrong answer. Can you please help, am i still doing something wrong
     
  5. Jun 17, 2008 #4

    Dick

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    vsound/vobject=1/1.5. I don't get sin(theta)=1/1.5 giving me theta=0.8867. Can you check that? And tan(theta)=height/distance traveled, right?
     
  6. Jun 17, 2008 #5
    i converted mach to meters a second but if i use 1/1.5 i get 0.73 degrees for theta. Using this i got 3171.18m for the horizontal distance. Now do i use time = distance/velocity, and if so do i keep the speed in mach or meters a second
     
  7. Jun 17, 2008 #6

    Dick

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    I'll take 0.73 radians (NOT DEGREES) as a correct answer. But I still don't get your horizonal distance. Keep the velocity in m/sec. Mach is a ratio, you can't divide distance by mach and get seconds.
     
  8. Jun 17, 2008 #7
    i still get the same horizontal distance. I use tan theta = opposite/adjacent, which i rearrange to tan theta x adjacent = opposite, so tan 0.73 x 5029 = 4500.54. Is that right because i still get the wrong answer
     
  9. Jun 17, 2008 #8

    Dick

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    Opposite=5029m, right? It's the height. distance=5029m/tan(theta). theta is the opening angle of the cone, innit?
     
  10. Jun 17, 2008 #9
    ohh, i didnt pick up on the rearranging error. Now I get the horizontal distance to be 5619.51223. Is that right. Then if i divide that by 442.5696 (which is mach 1.5) i get 12.70, but the correct answer is 11, am i still doing something wrong? do i use taht equation?
     
  11. Jun 17, 2008 #10

    Dick

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    Have you thought about taking your calculator in for a tune-up? You never seem to get the same numbers I do. Mach 1.5 is (343m/sec)*1.5. I get 514.5m/sec, not 442.
     
  12. Jun 19, 2008 #11
    thanks. I got the right answer....in the end. I was using a converter for the mach to meters a second conversation thats why i got it wrong. But thanks for the help
     
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