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Need Help Designing Speaker Enclosure/Engineering

  1. Dec 31, 2014 #1
    Hello all, first post here to physics forums and I have a lot to learn. I will be attending a northern Ontario university for Mechanical Engineering in fall so hopefully this relationship proves fruitful.

    Here is my problem, I bought a new stereo for my jeep.. and I am having trouble designing a closed baffle enclosure for my 10.1'' subwoofer.

    Here is where I am and how I got there, and why I am having trouble...

    Given:
    Fs = resonant frequency = 33.5 Hz
    Cms = mechanical compliance = 0.0002m/N (metres / Newton)
    Sd = effective area of cone = 0.0415m^2 (metres squared)

    Unknown:

    Cas = Acoustic Driver Compliance Cas=Cms*Sd^2
    Cab = Acoustic Box Compliance Cab=Cas *R\
    R= driver to box compliance ratio
    R = 2

    So: Cas = 0.0002m*(0.0415m^2)^2
    =0.0002m/N*(0.00172225m^4)
    Cas = 3.4 * 10 ^-7 m^5/N

    Therefore Cab = 3.4 * 10 ^-7 m^5/N divided by two
    = 1.72 x 10^-7m5/N

    Now Volume of the Box Vb = Cab *Gamma Constant (Lets assume it is 5.77)
    Vb = 1.72 x 10^-7 m^5 /N * 5,77
    Vb = approx .99 x 10^-7m5/N

    ^^^^NOW HERE IS MY ISSUE^^^^

    How the hell am I coming up with such a wrong answer, surly area is not expressed in terms of M^5/Newton and why is my volume so high? The Manufacturer recommends an enclosure from 0.08 m^2

    please HELP, I will greatly appreciate it and contribute as much as I can to this forum :)

    Also I am fresh out of high school took a year off, and its been 2 years since high level Math or Physics courses so please excuse me if the mistake I am making is pity.
     
  2. jcsd
  3. Dec 31, 2014 #2
    Hi Chris, and welcome to PF!
    I checked the Thiele/Small parameters page on Wikipedia to look at the equation (which I did not know by heart), and my quick calculation with your numbers yielded an equivalent compliance volume that is 49 liter. I will post my calculation here in a while...

    EDIT:
    According to wiki, the equation is

    Vas = ρ * c2 * Sd2 * Cms

    and with your values above, this yields

    Vas = 1.184 * 346.12 * 0.04152 * 0.0002 m3 ≈ 0.048852 m3 ≈ 49 liters.
     
    Last edited: Dec 31, 2014
  4. Dec 31, 2014 #3

    Thank you so much! If you could post your solution I would greatly appreciate it, I know there are other ways but I found the thiele parameters easy.. I'm sure that won't be the case for my mid frequency and tweeter drivers.
     
  5. Dec 31, 2014 #4
    I noticed something in your calculations , shouldn't it be p * c^2 * (0.0415m^2)^2 * 0.0002m/N? Which leaves me in the same confused state as to what to do with newtons
     
  6. Dec 31, 2014 #5

    jim hardy

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    2016 Award

    Maybe, just maybe, if we resolve everything to mass, length and time:

    Newton is force which = ma so it could have units mass X length/time^2

    so
    Vas = ρ * c2 * Sd2 * Cms


    rho would be mass/length^3
    c^2 would be length^2/time^2
    Sd^2 would be length^4
    Cms in meters per newton would be length/(mass X length/time^2) equals time^2/mass

    so i get for units of Vas

    [mass/length^3] X [length^2/time^2 ] X[length^4] X [ time^2/mass]

    which has for numerator = mass X length^2 X length^4 X time^2
    and has for denominator = length^3 X time^2 X 1 X mass

    so mass cancels
    time^2 cancels
    all that's left is length^3 which is volume.

    use 'em to get rid of that pesky velocity and mass

    hope above helps

    old jim
     
  7. Dec 31, 2014 #6
    Thank you sir, I had forgotten all about dimensional analysis. I was a bad student in grade 12, often stoned for the majority of physics so I don't recall much. I did much better in grade 11, and since have learnt my lesson that smoking everyday is something my brain can no longer do if I wish to keep what intelligence I have left, let that be a lesson to some.

    Thank you
     
  8. Dec 31, 2014 #7

    jim hardy

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    Science Advisor
    Gold Member
    2016 Award

    I sacrificed quite a few brain cells to beer and won't cast stones.

    Glad to see you digging into speakers, they're really interesting.

    Have fun
     
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