In a conventional loudspeaker, is the dampening force proportional to the velocity of the cone? In many other mechanical systems I have heard this is close enough to say true. It seems as if this is true in the case of the speaker, one could get a rough modeling idea of what the speaker is doing by the following differential equation:
(Mmd)*x''(t) + (beta)*x'(t) + [1/(Cms)]*x(t) = [V(t)/Z]*{magnitude(L x B)}
where Mmd is the mass of the system, beta is some dampening constant, Cms is the compliance of the suspension, V(t) is the voltage as a function of time, Z is the frequency dependant impedance of the woofer, L is the length of the voice coil's wire in the magnetic gap, and B is the strength of the magnetic field in the gap.
Now solving the homogeneous system associated with this would be very easy, provided the damping force of the system is proportional to the velocity of the cone as assumed in the above eq. What worries me is the non-homogeneous term (the applied force), which includes an unknown function of time, V(t) and a frequency dependant impedance. I'm not so sure where to go with that...
Also, once a system like this is solved for x(t), it seems as if there would be a way to go to model the low frequency roll-off of the system. I was thinking that using a Fourier transform of some nature with the applied voltage consisting of sinusoids at all frequencies would bring me to where I want to be. Now the thing is I don't really know anything about the Fourier transform except what some EE friends of mine have briefly shown me; I also don't know how to model V(t) as a function consisting of sinusoids at all frequencies, or the impedance as a function of frequency. Also, it seems as if I'm "begging the question" with impedance in this case...it seems as if I'm modeling something that will determine impedance using the impedance, so I'm not so sure I can just start with that in the original differential equation.
Can someone help me out here? I feel like I'm just about there, but am missing some piece of the puzzle...keep in mind I have no math knowledge beyond very simple ordinary differential equations or physics knowledge beyond a first course in electromagnetics. Thanks
Posts: 3956 | From: State College, PA | Registered: Sep 2000
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This link maybe of use web page read all of those,those are definately similar to what your talking of.
although i have only started getting into the real physics of this,i can see a point to knowing it,so far it seemed pointless to know boring maths and physics
lately ive been modeling basshorns,and will construct one very soon...
its important to know all the backround.
Try audioasylum.com , Wayne at the pi forum should answer you if no one else does.
and yes i have used FFT On cooledit2000 to see the bass quantity in songs i have-i used it,i know its measuring the amount of sinewaves at every frequency,i leave it at that
posted
Rybaudio, I've been reading up on this subject lately, and the method that appeals to me the most concerns modelling the electrical, mechanical, and acoustic system with an electrical circuit.
I have a great reference if you are interested.
Good Luck, Ash
-------------------- ****************************** ****************************** Posts: 1130 | From: Los Angeles, CA | Registered: Aug 2001
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posted
Yeah...since I've posted this I've been able to figure out many parameters doing just that. I've been able to see where the raw parameters of the driver come from, now just to learn how the modeling of enclosures comes about, which again I'm pretty damn sure can be modeled with an electrical circuit. Interesting stuff really...never thought it would have been this simple.
Posts: 3956 | From: State College, PA | Registered: Sep 2000
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posted
its alot more simpler than i thought! AC theory basically.
winisd says= Voltage source, Uad, is so called "constant pressure generator". Resistance models acoustic resistance, capacitor models compliance (volumes) and inductor models mass. There are several ways to determine component values. One, which is used in WinISD pro, is where we start on driver Vas to determine Ccas:
Ccas = Vas/(roo·c²)
Then, we'll use fs to determine Lmas:
Lmas = 1/((2·pi·fs)²·Ccas)
Then, Qes and Qms is used to determine Rae and Ram:
Rae = 1/(2·pi·fs·Qes·Ccas) Ram = 1/(2·pi·fs·Qms·Ccas)
Now, we'll calculate box volume modelling capacitor Ccab just like Ccas. If we have closed box, we'll have only determine the leak and absorption modelling resistors. These are determined by so called Q-factors. For lack of better models, these are determined at resonance frequency of boxed driver.
Determining frequency response When all component values are in place, then we'll just simulate completed circuit, using any circuit simulation program, e.g. SPICE (Simulation Program with Integrated Circuit Emphasis). Frequency response is calculatable from determining the volume velocity through Ccab. Using one well-known relation, we can get to far-field pressure value from volume velocity:
p(r) = roo·s·U0(w)/(2·pi·r)·exp(-j·k·r)
where k is so called wave number (k=w/c), and r is distance from diaphraghm. U0 is total volume velocity produced by box. If there is only one chamber, then U0 is current through Ccab. If there are several chambers, like in bandpass enclosures, then total volume velocity is vector sum of all volume velocities of chambers. Latter exp()..-part is the phase factor (which has always gain of unity), which is neglected in WinISD, in order to show more clear graph. Pressure is therefore complex valued. Now, when we have obtained absolute pressure level, we may use reference pressure of 20 µPa, the 0 dB reference.
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