Need Help Designing Speaker Enclosure/Engineering

[Chris Larabee]

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.

 

[DennisN]

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

V_as = ρ * c² * S_d² * C_ms

and with your values above, this yields

V_as = 1.184 * 346.1² * 0.0415² * 0.0002 m³ ≈ 0.048852 m³ ≈ 49 liters.

 

[Chris Larabee]

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

V_as = ρ * c² * S_d² * C_ms

and with your values above, this yields

V_as = 1.184 * 346.1² * 0.0415² * 0.0002 m³ ≈ 0.048852 m³ ≈ 49 liters.

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.

 

[Chris Larabee]

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

V_as = ρ * c² * S_d² * C_ms

and with your values above, this yields

V_as = 1.184 * 346.1² * 0.0415² * 0.0002 m³ ≈ 0.048852 m³ ≈ 49 liters.

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

 

[jim hardy]

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

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 * Cmsrho 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.

Which leaves me in the same confused state as to what to do with Newtons

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

hope above helps

old jim

 

[Chris Larabee]

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 * Cmsrho 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

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 learned 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

 

[jim hardy]

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