What happens when 2 independent waves go through the same air? Do they both pressurize it? What happens when both of them meet a membrane? Do they both force it to vibrate? Does vibrating with 2 frequencies membrane cause Doppler effect?
If a full range speaker produces no Doppler, it suggests that a separate tweeter and woofer does produce some intermodulation... ? (with or without the membrane?)
We have a box with round hole covered by membrane. Inside of the box we have 2 independent sources of waves, one with 10 Hz frequency, another with 2 KHz frequency. Obviously, since sources of sound are separated there is no Doppler effect. Right?
Sure. (you're suggesting theoretically pure pressurization or something right (zero velocity))
But membrane that cover the hole in the box vibrates with both frequencies. Does it produce Doppler effect?
Sure. I think it would even if you left out the membrane, which you're probably hoping has no velocity difference from the air on either side anyway, right?
Wish I had a real spectrum analyzer or knew how to import an audio file into a good software one.
Sure. (you're suggesting theoretically pure pressurization or something right (zero velocity))
But membrane that cover the hole in the box vibrates with both frequencies. Does it produce Doppler effect?
Sure. I think it would even if you left out the membrane, which you're probably hoping has no velocity difference from the air on either side anyway, right?
Wish I had a real spectrum analyzer or knew how to import an audio file into a good software one.
Well, it would seem from the explanations that something like a backloaded horn, with little piston action and more compression, or an electrostatic which compensates for lack of excursion with area, would produce less doppler effect in the most sensitive region for phase and slight pitch changes? So FR "wins", or at least most kinds of FR.
Yes, I suggest now that there is no membrane anymore.
Just a hole. Let it be a hole in the wall that separates 2 independent sources of waves from the listener on the other side. Does the listener hear Doppler effect when the hole present?
Good article, too bad even a mathematical proof won't prove anything to non believers
By the way I didn't get the impression that the author was unsure of his calculations or understanding ?
Err,
Frequency modulation doesn't cause a "broadening of the HF centre", frequency modulation produces discrete side bands just like IM distortion does, except it produces multiple sidebands for a single modulation frequency instead of just a single pair. (Have a look at at any text on frequency modulation)
In fact the first sidebands for FM are f1-f2 and f1+f2, eg exactly the same sum and difference frequencies as the 2nd order IM products.
This is mentioned explicitly by Linkwitz in the article I linked earlier, he also goes on to point out that intermodulation sum and difference side bands are in phase with each other while FM sidebands (at the same frequencies) are out of phase with each other.
Thus the type of distortion can be distinguished by the relative phase of the sidebands, and having both types present in similar quantities will cause one sideband to add and the other to subtract, leading to unequal amplitude sum and difference frequencies
Quote:
"The sidebands occur at the same frequencies fH - fL and fH + fL as the 2nd order intermodulation products of the two tones. They can be differentiated by changing the applied signal levels. Doppler sidebands decrease 3 dB for a 3 dB reduction in signal levels, whereas 2nd order intermodulation sidebands decrease 6 dB. The two sidebands may be of different amplitude when both forms of distortion are present, because the intermodulation products are in-phase with each other, the FM sidebands are out-of-phase. This fact allows a decomposition of unequal sidebands into their two constituent odd and even parts. "
http://www.linkwitzlab.com/frontiers.htm#J
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Good article, too bad even a mathematical proof won't prove anything to non believers
This article is NOT addressing the idealized speaker that I have been referring to. In fact, it's opening statement says: "The excursion introduces harmonic distortion even when the piston is vibrating with a pure sinusoidal motion at a single frequency". This article introduces additional considerations that makes it a non-linear system. Without that non-linearity there would be no IM distortion. It looks really interesting and I would like to read it through again. It may be an explanation for why people measure what they think is Doppler shifts in speakers.
I wonder if you and I have been talking cross purposes ? - my definition of an idealized speaker is one in which a single applied sine wave produces a single tone of sound and the 'argument' is over the case where two tones result in Doppler shift.
Yeah, as soon as you start to freq. modulate you change the shape of the sinusoid into something else. As soon as it's no longer a sine wave it gets ugly fast.
At the same time, Wavebourn does describe roughly what the spectrum would look like. When you think about a relatively low modulating frequency compared with the HF,
The woofer spends more time moving slowly (when it's changing direction) than moving quickly - just like a pendulum. So the Doppler shift doesn't produce a uniform smearing of the HF. The main sidebands will be all bunched up around the carrier but if you look at it with your bad eye it will look like a broadened HF.
And its another cautionary tale about maths. The complex math of FM is dealt with using Bessel functions and usually people simplify their analysis to their amplitudes and picturing the spectrum as a set of simple infinitely narrow spikes. But the reality is a more complex, there is width to the sidebands, Bessel functions are a smoothly varying function.
I suspect everything that moves does, including the air, the cone, everything.
What's important is the maximum instantaneous velocity, which will be Aw (where w is omega, 2pi*f).
For my little Tang Band woofers, that will move ~20mm p/p without thinking twice, the velocity of the cone gets rather high compared to that of a speaker moving only a couple of mm.
The air immediately in front of the cone is also moving back and forth with the cone (assuming reasonable coupling).
The air a few metres away will be moving a tiny amount, as the sound energy quarters per double of distance. Lets say it's 0.1mm one way.
If our ear drums were well coupled to the air, they too would move a similar distance.
Now, all of the above are transmitting a LF signal. When a higher frequency signal rides on top of it, the HF signal is, I suspect, being modulated in every case, but in the case of the more distant air and our ear drums, their amplitude is small, and so their maximum velocity is negligable compared to the speed of sound.
When two frequencies are present, we can never say there's no modulation of any form, but we can say it'll be so small we don't need to worry about it.
Chris
If you check back through my posts there is one where I did mention that the displacement of the acoustic centre with excursion does in theory produce a very tiny amount of phase modulation of the low frequency signal itself (not just of a 2nd high frequency) - in other words even a single sinusoidal bass tone reproduced by a speaker will be very slightly distorted by the fact that the acoustic centre of the speaker is not the same distance from the listener over the entire cycle.
Because the amount of phase modulation is proportional to frequency, at the low frequency where the excursion is occurring it is VERY small. What the guy in that article has done is calculated precisely how much it is, and from memory in his particular given example the distortion products were below -80dB - in other words totally insignificant, yet still real.
His maths demonstrate that a perfectly rigid piston moving with a perfectly sinusoidal motion towards and away from the listener does NOT produce a perfectly sinusoidal SPL at the listening point - it will be slightly distorted even though only one input frequency is present, and the reason why is because the distance between diaphragm and listener is changing during each cycle.
I think this is a really important point.
Your definition of an idealised speaker could only be met with a diaphragm of infinite cross sectional area which would also have zero excursion. As soon as a diaphragm has excursion it is no longer idealised by your definition and it will no longer produce a single tone in response to a sinusoidal movement, no matter how small that distortion might be it is non zero, and derived in the maths of that article. (Maths that is well over my head to analyse, although I understand the concept behind what the maths is showing perfectly)
However only when two widely separated tones are present at once does the theoretically present but practically unimportant distortion rise to a level where it is (a) measurable on a practical driver in amongst all the other distortions and (b) become potentially audible.
To be honest I think unless a driver is ultra low distortion with an exceptionally well designed motor FM/doppler distortion is going to be completely swamped by normal IM distortion / AM modulation from BL(x) and Le(x) etc, so in the grand scheme of things its not that important unless you've got rather large excursions from an otherwise very linear, small diameter wide band driver.
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Thank you Chris;
now I am happy to know that my line arrays produce much smaller amount of distortions than big full range speakers!
What we learned from this discussion, distortions generated by speakers are similar to distortions generated by an air itself. That means, the higher are they, the louder sounds seem to sound. The lighter and bigger is radiating surface, the less of distortion of dynamics we perceive, but with better speakers some music may seem to sound less dynamic: less variations of imaginable loudness. I like tall narrow line arrays exactly because it expands less apparent loudness variations beyond sound pressure variations that ordinary speakers do. I paid attention on this effect first time when one my guest turned up volume of my system way beyond of what he used at his home. Probably he tried to match distortions to the level he got used to, it was my conclusion.
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