1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Changes in Decibels over a distance

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data

    A jet plane emits 3.0×105 J of sound energy per second.
    1) What is the sound level 21 m away?
    2) Air absorbs sound at a rate of about 7.0 ; calculate what the sound level will be 5.00.
    3) Calculate what the sound level will be 7.50 away from this jet plane, taking into account air absorption.

    2. Relevant equations

    J/s = W
    inverse law of intensities: I_1*(r_1)^2=I_2*(r_2)^2
    dB = 10log(I/I_o)
    I_o = 1.0*10^-12

    3. The attempt at a solution

    My attempt at a solution is poor, I know, but this is the first problem like this ive come across.

    I had no idea how to relate Joules per second to decibels, so I did the 1:1 conversion to Watts. Still having no idea how to relate watts to decibels, I used an online watt to decibel conversion engine. This gave me 300000 W = 54.8 dB, so I set off running with it.

    From there I plugged 54.8 into the decibel formula:

    54.8 = 10log(I/I_o) ---> 5.48 = log(I/I_o) ---> 10^5.48 = I/I_o
    10^5.48 = 301995.172 ---> 301995.172 = I/I_o
    I_o = 1.0*10^-12 ---> 301995.172*(1.0*10^-12) = I
    I = 3.01995 * 10^-7

    Using this intensity as I_1, and giving this initial intensity a distance of 1 from the jet, I plugged it into the inverse law of intensities:

    I_1*(r_1)^2 = I_2*(r_2)^2
    (3.01995*10^-7)*(1)^2 ---> 3.01995*10^-7 = I_2*(r_2)^2
    3.01996*10^-7 = I_2*(21)^2 ---> (3.01995*10^-7)/441 = I_2
    I_2 = 6.847959*10^-10

    Then, I plugged this intensity value into the decibel equation, thinking it would give me the decibel level at 21 m:

    dB = 10log((6.847959*10^-10)/(1.0*10^-12))

    After calculating this, I got a value of 28.121 dB for part 1.
    Unfortunately, masteringphysics has told me this is incorrect, and so I am out of ideas as to how to solve part 1, also rendering me incapable of solving parts 2 and 3. :mad:

    Any help would be greatly appreciated.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted