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MCQ about intensity of sound waves (formula manipulation)

  1. Dec 21, 2012 #1
    1. The problem statement, all variables and given/known data

    jts37a.jpg

    2. Relevant equations

    The equation that is already given + (maybe) I is proportional to A2f2.

    3. The attempt at a solution

    I took the square root of 8, 8 being the Amplitude and I being proportional to the square of A. (I make the constant of proportionality 1). That's not the answer.
     
  2. jcsd
  3. Dec 22, 2012 #2

    SammyS

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    If [itex]\ \displaystyle I\propto\frac{1}{x^2}\,,\ [/itex] then [itex]\ \displaystyle I=\frac{k}{x^2}\,,\ [/itex] where k is the constant of proportionality.

    This means that [itex]I\cdot x^2=k\,,\ \text{ a constant}\ .[/itex]

    Added in Edit:

    This is wrong. See correct response below.
     

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    Last edited: Dec 22, 2012
  4. Dec 22, 2012 #3
    Obviously, but we can't find k here because we don't have a numerical value for x OR I.
     
  5. Dec 22, 2012 #4
    You don't need to calculate k.

    At point P, we have I=k/r^2
    Write a similar expression for the intensity at Q and compare it with the above expression.
     
  6. Dec 22, 2012 #5

    SammyS

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    You are given an amplitude, A, at point P.

    Also, [itex]\ \displaystyle I\propto\frac{1}{x^2}\,,\ [/itex] and [itex]\ \displaystyle I\propto{A^2}\ .\ [/itex] This means that [itex]\ \displaystyle A\propto\frac{1}{x}\,,\ [/itex] assuming they're both positive. Therefore, Ax = k, where k is some constant.

    You don't need a numerical result for k.

    Ax at P

    is equal to

    Ax at Q .



    @ P, A = 8μm and x = r .

    @ Q, x = 2r , what is A ?
     
  7. Dec 24, 2012 #6
    A is inversely proportional to x. So if A is doubled, x will be two times less. So if A at x is 8, A at 2x will be 8/2 which is 4.

    Thanks!
     
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