[Roger A. Modjeski]

Here's the question. What makes a dynamic driver (moving coil cone speaker) have flat frequency response over it's range of comfort as defined on the bottom end by resonance of the driver in it's enclosure and the top end by cone break-up.

All answers are welcome or would you like multiple choice?

[jimdgoulding]

The crossover, I expect, with the capability of the drivers selected.  Something is to be said about the enclosure, too, me thinks. 

[JackD201]

What exactly do you mean by "range of comfort"? 

[JohnR]

A lot of drivers have a rising (on-axis) response in that range. However I'm guessing the answer is the inductance of the voice coil?

[tubegroove]

I am guessing its the materials that make up a speaker cone itself like the cone material, glue used, suspension, the magnet, dust cap etc etc and perhaps also the crossover design and parts...

[Roger A. Modjeski]

Thanks for giving it a go. Remember the answer lies in physics, not materials.

Range of comfort is defined as resonance in the box on the bottom end and cone breakup on the top end. A 6.5 inch driver can be made that will resonate around 40-60 HZ in a sealed box. Depending on cone material and cone shape it will start to break-up around 1-2 KHZ, but we stop before that happens. So within those octaves there is a principle of physics that causes the driver to have flat response. In this range the quality of materials does not matter. A driver that can be had for 99 cents will behave the same as far as having flat frequency response in that range as one that costs $ 99.00 or $999.00. I'm not saying they will sound exactly the same but they will both have flat response. The question is WHY?

[Roger A. Modjeski]

A lot of drivers have a rising (on-axis) response in that range. However I'm guessing the answer is the inductance of the voice coil?

Good point, that is due to the fact that the driver is more directive when the wavelength it is producing approaches the cone diameter. That is also why a big driver should crossover lower than a small one. One problem of 2 way speakers is that transition from a large woofer to a small tweeter. The directivity change can be very large when going from a 12 inch woofer to a 1 inch tweeter at 1-2 Khz. If you are listening off axis it's especially bad as the woofer beams at you up to the crossover point iin the woofer then the tweeter suddenly gets wide above the crossover point. The off axis listener gets quite a different sound from the on axis listener. Of course having smaller drivers, as is now the practice helps this but the problem remains to some extent.

No wonder many speakers have a single sweet spot. It's a real challenge to make a speaker have a wide horizontal listening zone. Just look at how rooms are set-up at shows. There is an ESL maker whose speaker is so directional the seats are only one wide and 4 deep where others are 4 wide and 2 deep.

BTW, voice coil inductance causes the current in the voice coil to decrease which helps reduce the rising response due to directivity, however it doesn't change much up to the typical crossover point so it's above the "range of comfort". The term in bold is a hint to the answer. One can ignore the inductance.

[cujobob]

Isn't this the idea behind using a large waveguide to match the directivity of the woofer?

[richidoo]

Flat impedance.

[Clio09]

Roger, I'd be interested in your opinions on the use of a 90 degree wave guide as in my speakers, which are two drivers crossed over at around 1.7kHz.

http://audiokinesis.com/product_ak_jazz-module.html

They are made for off axis listening, in fact toe-in is recommended so that the axis crosses a couple feet in front on the listener (I toe mine in 45 degrees which is okay by the manufacturers recommendations). A benefit is I get a larger sweet spot with uniform response.

Regarding the ESL's you referenced. If I'm guessing correctly on the manufacturer, the speakers are also set up on the diagonal of the room (at least they have been last few times I heard them at shows). If this is the same manufacturer I can say that I do like what I hear in that set-up, but it's somewhat unrealistic in comparison with what many of us, including myself would want in our listening rooms.

[Roger A. Modjeski]

Flat impedance.

Flat impedance is a result of the physics not the cause.

Here are some more hints: Remember I am discussing a single driver, a woofer in this case so we are only concerned with the motion of the cone and voicecoil. If you like let's make the range start an octave above resonance and and stop an octave before any cone breakup starts. This still gives us four octaves of excellent behavior form say 100 Hz to 800 Hz in which even an inexpensive driver behaves very well.

In those four octaves the impedance of the driver is resistive for all practical purposes.  In fact the back EMF is so low that the impedance of the speaker would be the same if the voice coil is locked and the motion of the cone would be the same in a vacuum. That is a big hint.

[stereocilia]

My guess is that the frequency response will be flat if the suspension obeys Hooke's Law of elasticity through the operating range.

[JohnR]

Oh, you're saying that it's because the acceleration of the cone with frequency (for a given input voltage) is constant?

[Duke]

What makes a dynamic driver (moving coil cone speaker) have flat frequency response over it's range of comfort as defined on the bottom end by resonance of the driver in it's enclosure and the top end by cone break-up.

Assuming a direct-radiator speaker, if the linear displacement of the cone quadruples with each halving of frequency (or decreases by a factor of 4 for each doubling of frequency), the on-axis response will be flat but the power response probably will not be.  This same relationship can be expressed in different terms.

This relationship between displacement and on-axis SPL changes with various types of horn loading. 

[Roger A. Modjeski]

Oh, you're saying that it's because the acceleration of the cone with frequency (for a given input voltage) is constant?

Yes the acceleration is constant. You are on the right track. Now consider Newton's second equation F=M x A. Rearrange it to find the thing you want.

[Roger A. Modjeski]

Assuming a direct-radiator speaker, if the linear displacement of the cone quadruples with each halving of frequency (or decreases by a factor of 4 for each doubling of frequency), the on-axis response will be flat but the power response probably will not be.  This same relationship can be expressed in different terms.

This relationship between displacement and on-axis SPL changes with various types of horn loading.

To keep this simple I want to just consider the on axis response as read on an SPL meter at a few inches from the cone. That is pretty much what the speaker makers are looking at on their computers when they draw their curves. Remember just a single driver. John Atkinson often shows the plots of the drivers separately.

[stereocilia]

It's been way too long since I thought about Kinematic Equations and what not; so I'm out of my comfort zone.     I'll keep reading, though.

[Roger A. Modjeski]

It's been way too long since I thought about Kinematic Equations and what not; so I'm out of my comfort zone.     I'll keep reading, though.

It's really not that hard. Try the rubber band and weight experiment.

I just learned the other day that JBL had for all it's early years till the 1970s, been using an opposite convention for phase from the entire industry (I am guessing on the date).  The link below is their technote on how they are going to deal with it.

http://www.jblpro.com/pub/technote/tn_v1n12b.pdf

[stereocilia]

True, it's not that hard.  But, It feels more difficult when my goal is to understand it just for its own sake.  I'm not engineering loudspeakers, so for this I am content to be walked through the answer.

The polarity reversal thing reminds me of early tractors that use a positive ground.  I suppose you could think of them as using positrons instead of electrons as currency.

[Uptown Audio]

effective mass