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Decibel questions, how many people are cheering

  1. Sep 18, 2007 #1
    1. The problem statement, all variables and given/known data
    In a neighborhood challenge to see who can climb a tree the fastest, you are ready to climb. Your friends have surrounded you in a circle as a cheering section; each individual alone would cause a sound intensity level of 80 dB at your location. If the actual sound level at your location is 87 dB, how many people are rooting for you?


    2. Relevant equations
    Not a clue.


    3. The attempt at a solution
    The book reads 5 as the answer, how would we get this though?
     
  2. jcsd
  3. Sep 18, 2007 #2
    Do you understand what a decibel (or even, a bel) is?
     
  4. Sep 18, 2007 #3
    Yes, but without actually using the logs or taking the reverse of a log to get the answer, would there be a easier way to get it. i am just looking for the way to get the answer!!!!



    BEL= log base 10 I/Io
    DECIBEL= 10log base 10 I/Io


    ... Now... how would i obtain the answer?
     
  5. Sep 18, 2007 #4

    mgb_phys

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    You don't actually need logs ( assuming you have a calculator that can do powers)
    You are looking for the ratio between the intensity of one person and the intensity from N people, dBs are designed to make it easy to do this calculation.

    You know db = 10 log I/Io so I/Io = 10 ^ ( db/10)
     
  6. Sep 18, 2007 #5
    Right, but I guess what I'm trying to say, is there a way or equation that adds a specific amount of decibels onto the original amount if they are all at the same amount of decibels.

    like for instance 5 people at 80 decibels comes out to 87 decibels. how would i get the 5?
     
  7. Sep 18, 2007 #6
    87 - 80 = 7db. 10*log_10(7) ~ 5.
     
  8. Sep 18, 2007 #7

    mgb_phys

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    Not quite
    87-80 = 7db and I/Io = 10^(7/10) ~ 5 and Io = 1 so I = 5
     
  9. Sep 18, 2007 #8
    Thank you.
     
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