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Sound Intensity Problem

  1. Jan 19, 2005 #1
    I am confused about a homework problem and was hoping that maybe somebody here can help......

    Homework Problem
    When a helicopter is hovering 1090 m directly overhead, an observer on the ground measures a sound intensity I. Assume that sound is radiated uniformly from the helicopter and that ground reflections are negligible. How far (in m) must the helicopter fly in a straight line parallel to the ground before the observer measures a sound intensity of I/4?

    According to my textbook, "If the distance increases by a factor of two, the sound intensity decreases by a factor of 2^2=4"

    So I figured that to find the answer I simply muiltiply the initial distance (1090m) by 2 so the sound intensity (I) decreases by 4 (I/4). When I do the math, my answer is 2180m but this is not the correct answer.

    What might I be doing wrong?

    Thanks in advance!
  2. jcsd
  3. Jan 19, 2005 #2


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    Homework Helper

    You have to use the pythagorean theorem. 2180m is the distance from the helicopter to the observer. But the question asks how far the helicopter flew horizontally. Draw a sketch...
  4. Jan 19, 2005 #3
    Thank you for the help!

    Ah ha, I see. Now my problem then becomes a basic algebra issue. I understand that the pythagorean theorem is A^2 + B^2 = C^2 and when I sub in the values I get as an equation:

    C^2=sqrt(A^2 + B^2) --> 2180^2 = sqrt(1090^2 + B^2)

    But I do not know how to solve for B^2 when A and C are both known. Can someone maybe help with my algebra on this one?

    I added a graphic to this thread that depicts the problem.

    Thanks again!

    Attached Files:

  5. Jan 19, 2005 #4


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    Science Advisor
    Homework Helper

    No,no,your formula expressing Pythagora's theorem is completely wrong

    [tex] 2180^{2}=1090^{2}+B^{2} [/tex]

    Solve for "B",knowing that only a positive solution si acceptable...

  6. Jan 19, 2005 #5


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    Homework Helper

    you inserted a wrong sqrt here. It should be:

    C^2=A^2 + B^2 --> 2180^2 = 1090^2 + B^2

    Solve for B here.
  7. Jan 19, 2005 #6
    Thanks for all the replies, I got it! I really did know how to do this (solve for B^2 that is), I must have just had a mental block as my brain has been on vacation for a month.

    1887.94 m.

    Thanks again!
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