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Total Power output by Speaker

  1. Jan 19, 2015 #1
    1. The problem statement, all variables and given/known data
    A speaker emits sound waves in all directions, and at a distance of 28 m from it the intensity level is 73 db. What is the total power put out by the speaker, in watts? ( reference intensity [itex]I_{0}[/itex] is 1.0 × 10-12 W/m2.)

    2. Relevant equations
    [itex] P= I*A [/itex]
    [itex]I = I_{0}*10^{B/10} [/itex]
    [itex]SA = 4*pi*r^{2} [/itex]

    3. The attempt at a solution
    Since we're looking for the total power of the speaker, I first used equation 2 to find the intensity, [itex]I[/itex]. For [itex] B = 73 db[/itex] and [itex]I_{0} = 10^{-12} W*m^{-2}[/itex] I obtained [itex] I = 2*10^{-5} W*m^{-2}[/itex] .

    Then the area is [itex] A = 4*pi*(28)^{2} m^{2} = 9852.03 m^{2}[/itex]

    Therefore, the total Power is
    [itex]P = I*A = 0.197 W[/itex]

    So that's my attempt but I'm still not entirely confident in that answer. I'm not too sure if the Area equation I'm using is correct. It says in all directions hence why I used surface area but now I'm thinking it's [itex] A = pi*r^2[/itex].

    Is that right? Or was the surface area equation the correct one to use?
     
  2. jcsd
  3. Jan 19, 2015 #2

    TSny

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    You were correct in your original calculation. Is there a reason why you were thinking that maybe you should use the area of a circle rather than the surface area of a sphere?
     
  4. Jan 19, 2015 #3
    I imagined the speaker on the ground, and then imagine the 'sphere' of sound in all directions. I didn't see it as a full sphere, so I thought the first equation wasn't right. Then I guessed it might just be a circle.
     
  5. Jan 20, 2015 #4

    TSny

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    OK. Does it make sense now?
     
  6. Jan 20, 2015 #5
    Yes it does. Thank you very much!
     
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