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Near and Far Field Attenuation Inverse Laws

  1. Mar 2, 2010 #1
    1. The problem statement, all variables and given/known data

    near-field distance attenuation follows an inverse cube law (1/d^3), while in the far-field it follows inverse law (1/d). Prove mathematically how we arrive at 60dB/decade from the inverse distance cube relation and 20dB/decade from the inverse distance
    relation.

    2. Relevant equations
    20 log (D) where D is the distance


    3. The attempt at a solution

    I'm pretty sure this problem is similar to control theory in converting magnitude to DB scale with 20 log (D). I can actually see the answer just by doing that; however, I'm thinking I'm missing the big picture somewhere by doing that. Mostly I can't seem to justify using the above equation.
     
  2. jcsd
  3. Mar 2, 2010 #2

    berkeman

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    Staff: Mentor

    What is log(1/d^3) ?
     
  4. Mar 2, 2010 #3
    Maybe I was thinking too much and thought there was more to the proof than just doing 20log(1/d^3) and 20 log (1/d). Thanks.
     
  5. Mar 2, 2010 #4

    berkeman

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    Staff: Mentor

    Glad to help. :biggrin:
     
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