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Thread: Check my algebra please (solve for Qms)

  1. #1
    Founding Member earthtodan's Avatar
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    Check my algebra please (solve for Qms)

    If Qts = (Qes*Qms)/(Qes+Qms)
    Or alternatively, (1/Qts) = (1/Qes) + (1/Qms)

    ...then am I correct in finding Qms by: Qms = (Qes*Qts)/(Qes-Qts) ?

    I made a little spreadsheet for determining sealed enclosure size recommendation, Qtc, and F3 using equations from the Loudspeaker Design Cookbook. I also added EBP. None of this involves Qms, but I thought I'd add that too just for fun. The problem is, when I looked at a bunch of driver spec sheets on Madisound, the Qms doesn't always agree with my spreadsheet. I'm usually close or in the ballpark, but sometimes it's just wrong. I thought there was a fixed relationship between these 3 terms, which means no other predictors from left field that could add uncertainty to this mathematical relationship. Why do so many manufacturer's specs not quite add up? Or is my math wrong?

    I'd like to be able to grow the spreadsheet in the future to derive qualitative sonic attributes from quantitative modeling.

    Dan
    Last edited by earthtodan; 01-24-2013 at 02:47 AM.

  2. #2
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    Quote Originally Posted by earthtodan View Post
    If Qts = (Qes*Qms)/(Qes+Qms)
    Or alternatively, (1/Qts) = (1/Qes) + (1/Qms)

    ...then am I correct in finding Qms by: Qms = (Qes*Qts)/(Qes-Qts) ?

    I made a little spreadsheet for determining sealed enclosure size recommendation, Qtc, and F3 using equations from the Loudspeaker Design Cookbook. I also added EBP. None of this involves Qms, but I thought I'd add that too just for fun. The problem is, when I looked at a bunch of driver spec sheets on Madisound, the Qms doesn't always agree with my spreadsheet. I'm usually close or in the ballpark, but sometimes it's just wrong. I thought there was a fixed relationship between these 3 terms, which means no other predictors from left field that could add uncertainty to this mathematical relationship. Why do so many manufacturer's specs not quite add up? Or is my math wrong?

    I'd like to be able to grow the spreadsheet in the future to derive qualitative sonic attributes from quantitative modeling.

    Dan
    Math is good.
    I would guess rounding error, but if you have specific examples post them up. Using values that are rounded can cause variation when calculating.

    So what is your interest in Qms if I might ask?

  3. #3
    Founding Member earthtodan's Avatar
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    You're right, rounding errors on either end could be responsible for minor deviations. Anyway, my equation agrees with WinISD autofill and my WT3 test results, so I'm good.

    I have no particular interest in Qms per se, I'm just interested in demystifying speaker physics and understanding the practical implications of T/S parameters. For example, the Cookbook gives an analogy of resonance and damping as a car suspension with a spring and a shock. The shock is the damper (Qts) that keeps the spring (Fs or Fc) under control. The higher the damping and/or the lower the resonant energy, the better a driver is suited for a sealed box, which makes sense because a closed air volume acts like a stiff spring. Thus, we have EBP = Fs/Qes.

    This is a great analogy but it leaves me scratching my head a bit. Why is Qms left out of the equation? Why are there exceptions, like the Peerless 830855 which has an EBP of 126 but is supposed to be suited to small sealed enclosures?

    Then you run across Internet tidbits like this:

    Drivers with a very high mechanical Q can sound more open, cleaner and have a better dynamic range. This is because they have less loss. The surround is more flexible, the spider is better constructed, they have better air flow and usually have higher sensitivity. So a high mechanical Q is a very good indicator of energy storage behaviour.
    I'd like to have the theoretical background to be able to verify or throw out claims like this. I'm also interested in growing my little spreadsheet so it can pop out these answers on its own.

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