"Speed" is a vague term. Do you mean acceleration or velocity?
…
^100%^
Usually people referring to slow or flabby etc. are usually talking about transcient response.
We don’t know if the OP means that, or not.
We should have them say what they mean.
"Speed" is a vague term. Do you mean acceleration or velocity?
Anyway, let's work it out from first principles. Let's define some terms:
- Displacement: how far the cone moves (meters)
- Velocity: how fast the cone moves (meters/sec)
- Acceleration: how fast the velocity changes (meters/sec^2)
For a given speaker driver producing a constant sine wave tone at a constant SPL:
- Frequency = ω/2π (ω = angular frequency in radians). Or: ω = 2πf. It is simpler to think of ω as frequency.
- Displacement follows this formula: x(t) = A * sin (ωt), where x(t) is the displacement of the cone at that moment of time, A is the maximum amplitude of displacement. Or put in plain English: the displacement of the cone equals the sine of the frequency (expressed in angular frequency) at that moment in time.
- Velocity is 90deg ahead of displacement (e.g. when the cone reaches the limit of its excursion, velocity is zero). So we take the cos function and multiply it by the angular frequency: v(t) = A * cos (ωt) * ω
- Acceleration is 180deg ahead of displacement (e.g. when displacement is at maximum, acceleration is at maximum but in the opposite direction). So we are back to a sine function. But to obtain acceleration, we have to multiply displacement by the square of the angular frequency. So a(t) = A * sin (ωt) * ω^2
If you want to ignore all that mathematics stuff, here is a simpler explanation:
- Frequency = 1 over time (1/s)
- Displacement is how far the cone moves (m)
- Velocity (m/s) is displacement multiplied by frequency
- Acceleration (m/s^2) is displacement multiplied by the square of frequency
Remember that SPL = the swept volume of the driver. Meaning, cone area * maximum displacement. So for a large driver to produce the same SPL as a smaller driver, it doesn't have to move as much (displacement is less). Looking at those equations again, if A is less, then so is maximum velocity and acceleration.
So yes, larger drivers are "slower" than small drivers if they are asked to produce the same frequency at the same SPL.
People talk about XMAX like it is the main thing to know, and I suppose that it is a straying to push the
Push the coil out of motor is not really a great idea.
In reality the SPL acronym has he “P” for “Pressure”.
There is no direct relationship for SPL to Position, Distance, or Velocity… it is all the 2nd derivative.
So we can sort of ignore position.
In the extreme, if we went to DC, we would see the motor providing a constant acceleration to “the cone”, which clearly have some limits.
(But there are rotary drivers)
In the operating range of a subwoofer, the pressure is
The Sound Pressure Level (SPL) can be related to acceleration and area through the formula: SPL = 20 log10(p/p0), where p is the sound pressure in pascals, which can be derived from the acceleration (a) and area (A) using the relationship p = ρaA, with ρ being the density of the medium. However, the direct SPL equation typically does not use acceleration and area explicitly
SPL = 20 log10(p/p0),
Or
SPL = 20 log10(ρaA/p0),
If we double the area (A) then we get to reduce the acceleration (a) by half.
Every motor is non-linear to some extent, but as the cone get larger and larger, then the total throw required gets to be less and less, and it is easier to stay in a more linear region as the throw approached zero displacement.
…
So yes, larger drivers are "slower" than small drivers if they are asked to produce the same frequency at the same SPL.
Yeah no.
More massive drivers are only slower at the same throw or velocity, using the same power/force.
Using a steady-state sine wave hides the transient behavior, that’s why the unit step signal or tone burst is used instead.
With a steady state sine-wave you can’t observe damping or any oscillatory behavior, even at resonance its still a sine-wave SPL, albeit larger.
If we use the example of a 0-60mph vehicle test, at T=0 the drive slams his/her foot on the accelerator, commanding the ECU for maximum torque (or in the old days wide open throttle) - in effect this is a step signal, and the response is the time it takes for the vehicle speed to reach a predefined amount… 60) or a stead state maximum (aka top speed). But now imagine the driver at T=0 only partially opens the throttle, then a second later, a bit wider and so on, a bit like your sine-wave example.
A shaped tone burst is also a good way of seeing the finite acceleration in the first half of burst cycle and indeed the overshoot when the burst is shut off. Siegfried Linkwitz provides a good explanation of how shaped tone burst are a great tool for examining transient response, and distortion too.
The Kicker data sheet has both step and tone burst performance.
Back to your “speed” definition if you have a small vs large driver and both have the same bandwidth, in the same enclosure type, do you think they have the same rise time from 0 to max?
In ^this example^, it may be better to think of the “speaker driver” as what happens at the instant when the throttle is mashed.
We don’t need the car or the cone to get up to 60 MPH, the pressure is instantaneous.
So it is more like “at the instant” when the throttle is matched the front if the car lifts up immediately. It doesn;t start moving and then the front end lift and the hind end squats down. It lift and squats immediately.
And on the cone, the pressure is instantaneous with the acceleration.[/QUOTE][/QUOTE]
