• Can't reproduce a square wave

1. What is a "square wave?" (in air)

2. What do you mean by "reproduce a square wave."

a. How do you "produce" a "square wave" (whatever that is) on a speaker to begin with?

b. How do you produce a "square wave" input signal (we know what that is, at least mathematically)to a speaker?

Mathematics can easily describe a square wave, but mathematics also assumes a continuous world. However, the world is not continuous, but discrete. Even if you assume that space and time are continuous, "air" is not, at least on the microscopic level. Mathematically a square wave is discontinuous, but the world (as seen by mathematics) is essentially continuous. However, a "shock wave" is a "discontinuity" in the air caused by something travelling through the air ***faster than the speed of sound in the air***. This almost closes the question right here. If you could make the piston of the speaker move any way you want it to (without consideration of how you do it), then what is the motion of the piston that would create a "square wave," whatever that is??

How do you produce a signal to the speaker that is a square wave signal? Certainly not with electronics. Electronics is closer to being continuous than air. A person throwing a switch on and off very rapidly could not produce a square wave signal, so certainly no transistor nor tube could.

The reason a square wave has long been used in Ham radio and electronics in general as a test signal is because on an oscilloscope, in order to look "good" a flat phase and amplitude was required to about to a factor of 10 X both ways from the fundamental.
It is an easy signal to see and any condition other than zero degrees phase and flat amplitude will not preserve this or any other complex waveshape.

Yes, it is true a Manger can reproduce a square wave (by eye as above) or other complex signal midband, I have measured one. (on the other hand they are also high in distortion).
Perhaps a different way to look at it that the speaker has essentially "no" spreading in time of the signal or zero group delay. You would think that a goal would be to preserve the waveshape but for the most part, speakers do not and for a number of reasons.
Some people are apparently sensitive to this, others not.
Cheers,

Tom Danley

Nice forum Wayne!

A square wave requires two well-defined potentials. Each half cycle is represented by a specific potential. In electrical terms, this is voltage, in mechanical, it is position and in acoustic or pneumatic, it is pressure. Here's the problem with the square wave thing: Even if you have a perfect piston driven by the perfect square wave, the pressure developed in open air dissipates.

If you are pressurizing a perfectly sealed chamber, you can keep pressure from dissipating, but not out in the open. Outside the speaker cabinet, it's like a very lossy system. That makes it act like a differentiator. So whether or not this is an issue worth noting is probably debatable. But making static pressure changes outdoors from a loudspeaker is pretty tough to do. It's easier to do as frequency goes up, but one could say it is impossible down low, at least without calling upon the Vogon Constructor Fleet from the Hitchhiker's Guide to the Galaxy.

It can be argued as you have in the past that in the home, a sound reproducer that preserves the waveshape of the input signal is not strictly necessary.

In sound cancellation however the exact waveshape must be produced if it is to cancel an offending noise. I have built transducers for this application as well and am familiar with what is involved.

It would seem the question of how much a speaker can screw up waveshape or corrupt the time element and still be listenable is separate from the conditions needed for preserving a complex input.

Your "creating a differentiated pulse" issue with this at low frequencies is based on an incorrect assumption. Radiating into space, the radiator motion (for a direct radiator) that produces an acoustic square wave is a triangle motion, not a physical square wave.
It is the radiator volume velocity that produces pressure and as long one is about 10 X higher than the low cutoff (owing to the requirements to have a good looking square wave), there is no problem going down in frequency and radiating a "square wave" assuming the flat pressure and phase region had sufficient bandwidth.
(at least from the stand point of having made acoustic sources systems which preserve waveshape down into the single digits)
Cheers,

Tom

Are you going to NSCA?

>> "Radiating into space, the radiator motion (for a direct radiator) that produces an acoustic square wave is a triangle motion, not a physical square wave."

That's my point. If you apply a square wave electrical signal to a loudspeaker cone, you will get movement of a physical square wave with constant displacement. Only if you modify the waveform, such that a constant displacement pump (loudspeaker) generates a constant volume can you generate an acoustic square wave.

I am not sure if we are talking apples and oranges on the square wave thing or not. What I am saying seems fairly obvious to me. You can't pressurize an open space with a constant displacement pump. The pressure dissipates. So you can't maintain pressure on alternate half cycles either. You can only hope to get an approximation at high frequencies.

An electrical square wave presented to a loudspeaker is the functional equivalent of a pump operating at a constant pressure in one direction, and then rapidly changing to the other. But loudspeakers energizing a large space are like a lossy system, in that you aren't able to maintain the increased atmospheric pressure on a compression cycle, nor can you maintain reduced atmospheric pressure on a vacuum or rarefaction cycle.

Electrical square waves presented to a loudspeaker make positive pressure on one half cycle and negative pressure on the other. The problem is that the pressure isn't maintained. It rapidly falls off. So the top of the square wave trails off, modifying it so that it looks like it has passed through a differentiator. At high frequencies, you can approximate an acoustic square wave but not at low frequencies, because pressure dissipates before each half-cycle has passed.

Modifying a square wave to create a triangular shaped signal will increasingly pressurize a room, so that the falloff from dissipation is counteracted by the increase from the rising wave. That sort of acts like pre-compensation by sending an integrated signal to the speaker, which pre-compensates for the differentiator formed by the dissipation falloff in pressure. The acoustic pressure can be made to resemble a square wave using this technique. But the signal presented to the speaker wouldn't be a square wave in this case.

If you are discussing real square waves, then you surely agree that they are impossible to produce electronically and acoustically.

But for Engineering purposes ("the second order term is small, so we ignore it" :), you mean something pretty "close" to a square wave. Now you are discussing speaker design philosophy, which is over my head, and I will butt out...

It is true that in extreme "fundamentalists" view, a square wave cannot be re-produced by any speaker, or even produced in the first place by any real world electronics, passed by any cable or be realized by physical action..
Every thing we deal with in the real world (outside of fundamental theory) has a high frequency limit and so a finite slew rate and so cannot instantly go from one value to another without traversing the area in between.

On the other hand, a square wave has been used in electronics as an analytical signal for at least a half century because it is simple to see and is effected by a signal bandwidth much much larger than the repetition rate suggests.
The rule of thumb in electronics is that one needs about a factor of 10 in flat amplitude and phase in each direction past the center frequency in order to have a good looking square wave on an oscilloscope (a standard instrument which displays a signal voltage over time).

This would mean that for a speaker that was flat in amplitude AND had zero degrees phase from 20 Hz to 20KHz, that it would satisfy the requirements of producing a square wave from about 200 Hz to about 2000Hz.
This would also be just as true for any part of the chain like a CD player or amplifier.

Part of what makes it useful is after learning to interpret it.
For example in a "simple" system, the rise and fall times are directly related to the high frequency response while any tilt in the "flat parts" is governed by the low frequency response. Phase shift will alter the position of the slew within the waveshape as well as determine the final shape.

While consideration of a square wave or the idea of preserving the waveshape of the input signal are two ways to look at it, there is another, that is time.

If one fed a speaker an imaginary signal that covered a wide frequency bandwidth and then looked at the sound as it emerged from the speaker, one finds the speaker spreads the signal out in time if it is not able to preserve the waveshape.
In other words, the original waveshape or impulse occupies X time, if the speaker cannot preserve the waveshape, it is also spreading the signal out in time and / or is altering the time relationships between various parts of the spectrum.

The Manger remains the "best" speaker in time I have ever measured although it is not a "clean" speaker or suited to high level operation unless one is insensitive to large amounts of harmonic distortion.

At least to me, I see anything that alters the original signal significantly as distortion, this includes the popular harmonic distortion, but also amplitude distortion and being dispersive in the time domain.
Cheers,

Tom

Inside a sealed box speaker, the pressure wave shape IS exactly related to the displacement. If one wanted a square wave pressure in a box, the cone has two positions, in or out with a fast transition between.
If you placed this box in an air tight room and operated it at a frequency where you are much lower than the lowest room resonance, one also finds the sound pressure out side the box IS also related to the displacement.

On the other hand, if one were in full or fractional space or in a room well above the lowest room resonance, then the conditions are different.
Radiated acoustic power from an acoustically small source (like a woofer) is NOT displacement but Volume velocity.

For a sine wave (easy to picture) signal, in a sealed box or acoustically small room (as above), one finds the pressure is "in phase" with the displacement.
Easy to imagine the woofer's outward position is compressing the air in the room etc.

Once one is outdoors or higher up in frequency in the room, one finds the radiated pressure is actually 90 degrees from the displacement,
That is to say, the greatest positive and negative radiated pressures coincide with the driver when it is at ZERO displacement (because that is where its radiator velocity (and there for volume velocity) is highest).

So far as audibility of waveshape preservation and adaptive crossovers, it turns out there are a few others interested in this.

http://www.ocf.berkeley.edu/~ashon/audio/phase/phaseaud2.htm

Here is a fellow on the same "non-integer" crossover path as used on the Unity's we discussed some long time back.

http://www.geocities.com/kreskovs/John1.html

If you are going to LasVegas for the NSCA trade show this week end, you could stop at our booth and hear a speaker that does a decent job with preserving waveshape (within band) and see if it sounds any different.

I would bet that it is the acoustic transition from pressure to volume velocity that is the part you refer to as a differentiator, I can see that it could look like that..
As in your (1st order) differentiator example, there is also the 90 degree phase shift going between pressure and volume velocity parts of the radiator motion

You are correct also that the piston motion does have to follow a path that results in a radiated "square wave" or other complex signal and that this is not the same shape as the acoustic pressure (because it is the volume velocity or Uo, not displacement or position which radiates acoustic power.)
For a square wave of any frequency radiated into some space (that is not acoustically small and contained), a constant radiated pressure requires a constant volume velocity, a constant velocity (with periodic reversals) traces out a triangle wave, that is the needed piston motion if radiating a square wave into space.
There is no frequency limitation on a square wave here other than (the bandwidth requirement as in the other post and) a pressure / frequency one set by the maximum displacement and driver linearity.

Cheers,

Tom