Originally Posted by goneten
. . . The deeper a driver plays the same SPL, the faster it moves. If you keep SPL fixed but drop the frequency, you increase cone velocity.
Sorry, but I believe you've said that backwards, probably inadvertently. Ignoring SPL, if the excursion is a fixed value x
, then the cone needs to travel a total distance of 2*x
in one cycle. If you drop the frequency in half, the cone will need to travel that same 2*x
distance in twice
the time. For 80 Hz, the velocity would average (80*2*x
), or 160*x
per second. for 40 Hz, the velocity would average (40*2*x
), or 80*x
per second. If you double the frequency, you double the average velocity.
. . . if you drop an octave in frequency from 80 Hz -40 Hz, the velocity must double as the duration in time for each cycle has doubled.
Again, if the duration in time has doubled, the velocity will be half.
I'm not sure I agree with you that velocity depends on amplitude.
If you increase the amplitude, you are increasing the distance that the cone need to traverse. If the frequency does not change, then the velocity needs to increase to traverse the increased distance in the same amount of time.
. . . If amplitude is fixed the acceleration of the cone is fixed . . .
. . . Velocity is an integral of acceleration.
Put another way, velocity is the derivative of position, and acceleration is the derivative of velocity. Discounting harmonic distortion in the speaker, if you are outputting a sine wave, then the cone's position, velocity and acceleration are all sine waves, each 90 degrees different in phase from the previous derivative. So if both amplitude and frequency
are fixed, then the acceleration of the cone is fixed. As frequency increases, velocity and acceleration increase proportionately. If amplitude increases, velocity and acceleration increase proportionately as well.
I'm pretty sure I learned the velocity/acceleration of the cone as a function of frequency/SPL from Dan Wiggins.
Yes, he would be correct. I think it is simply the direction
of the relationship that you have wrong.
I think we can all agree that mass has nothing to do with woofer speed. But if we take an 18" cone and an 8" cone, assuming identical excursion, the 8" cone will need to move further in the same amount of time to reproduce the same SPL.
Yes, the mass only effects the power needed to reach that SPL. And the 8 inch cone does
need to move further in order to match the SPL of the 18 inch cone.
So an 8" cone can't possibly move faster than a 18" cone assuming identical SPL and frequency, otherwise you've changed the frequency.
Again, you have the sign inverted. The 8 inch cone must
move faster since it needs to move further
in the same amount of time.
Now, I have certainly presented this in overly simple terms - the true behavior, especially the relationship to SPL, is more complex then I have described.