No. We would be forced to move by the same DC, if the membrane is infinitely large. Or, we would hear nothing if it is infinitely small.
I hadn't realised we were talking about an infinitely large membrane or an infintely small one. Just to be awkward, what if we stick with the 12 inch, perfectly rigid cone?
Or how about a 1" disc of titanium on a titanium plunger attached to a linear stepper motor fed with the equivalent sequence (in an arbitrarily long tube/bellows, or in free air?) - it's still a speaker in principle, presumably.
I think I'm beginning to get an inkling of what you're talking about.
If we wanted to actually synthesise the equivalent sounds of the following two conditions:
(a) a 10 kHz tweeter bolted to a 'woofer' being fed with a very low bass tone*
(b) a 10 kHz tone mixed with a very low bass tone*
What would be the difference between the two sequences we would feed the stepper motor? Or the voltages fed to a conventional speaker coil?
* The bass tone is so low and loud that at this point in its cycle, on its own, it would result in a constant cone movement of 1 m/s for an arbitrary time/distance.
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(It is this that I am referring to in condition (a) in my question above)
If I said that the sequence to the perfect stepper motor (at some arbitrary uniform sample rate) is
Step size = K + differential of 10kHz sinusoid
(or the equivalent, varying the time between uniform steps)
would that be (a), (b), neither or both...?
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In both cases, the output ought to be a 10kHz tone with some LF tone, +/- any modulation. Yet you're saying that the modulation will only occur in the latter set-up, where the membrane is carrying its own resonance.
Why should the case with the resonating cone be different from the case with the cone being driven at 10kHz?
Lets take a simple example with which we will all probably be familiar.
A car drives towards you playing some bass track (as they do). When stationary, the LF note is measured to be 30Hz.
As it drives towards you, the tone shifts to, say, 33Hz.
As it carries on past, it drops to 27Hz.
Now, so far as I can see, this counts as doppler distortion/frequency modulation/whatever else we want to call it.
The forces within the car have been summed mechanically.
The source is moving at significant (compared to 340m/s) velocity, and producing a tone whose frequency varies (about a fixed frequency, the one that the source is generating) with the direction altering the direction of the frequency shift.
Why can't that apply to speakers?
Chris
Do you mean phase issues with a driver crossover point? Or all the way through the audible spectrum? As in being out by 30* at 100Hz and 0* at 1KHz for example?
If it's the first one bin the passive crossover as they ARE the detrimental part of a 2+way speaker replace with active or digital and account for phase cancellations there.
Passive crossovers are the weakest link and should be binned and never thought of again it's because your FRs don't feature one that's why they sound better.
If it's the first one bin the passive crossover as they ARE the detrimental part of a 2+way speaker replace with active or digital and account for phase cancellations there.
Passive crossovers are the weakest link and should be binned and never thought of again it's because your FRs don't feature one that's why they sound better.
Because car moves in respect to the listener, while honk is applied in respect to the car. If to sum then apply driving and honking forces to the car in respect to some point outside of the car the result will be like in case of loudspeaker.
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nope, this is not what happens if the speaker is linear.
Most amplifiers put out a voltage signal and this produces a current flow through the finite resistance of the voice coil. Current flow through the voice-coil generates a magnetic field. This magnetic field interacts with the magnetic field of the permanent magnet to create a force between the voice coil and magnet. The voice coil is light and loses this battle - it moves, the magnet is stationary with respect to the listener. The force on the voice coil is directly proportional to the current flow, i.e. the signal. This force is opposed by the cone's suspension. Providing that all these things are well designed they can be considered linear and the cone will move a distance that is directly proportional to the signal. It's a giant ammeter in fact.
The cone moves relative to the magnet.
Of course, in real life there are non-idealities in the speaker, the suspension is not a perfect 'spring' etc. and such non-linearities can give rise to modulation products - and they may be measurable. But it's possible that such measurements are being ascribed to Doppler which I believe is incorrect (even if it's somebody famous saying it).
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Correct.
Not quite.
Depends on the frequency. Well below resonance in the "compliance controlled region" it is indeed the suspension that opposes the force from the voice coil.
However well above resonance in the "mass controlled region" (the majority operating range for most speakers) its the inertia of the cone's moving mass which opposes the force applied by the voice coil, and the suspension has almost nothing to do with it.
Not quite.
Again, it depends on the frequency of stimulation. Well below the resonant frequency (including DC) the force applied produces a displacement which is proportional to that force.
However well above resonance the acceleration of the cone is directly proportional to the force applied. (F=ma) This means that as frequency goes up the same amount of peak force causes progressively smaller excursion. (1/4 for every doubling in frequency)
The cone does not trace a movement that is directly proportional to the input waveform because of this, as well as the phase shift that occurs above and below resonance. (Well above resonance displacement is 180 degrees out of phase with applied force/acceleration)
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Exactly, my point. Thank you Bigun; it is a pleasure to have an experienced Professor on the forum, who can explain so simple complex things to students.
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Ah, I think I see now where your thoughts are coming from. Well, you describe the situation of a speaker as a damped resonant system. But this is not the Doppler effect though. It's the response of a driven harmonic oscillator. It will of course have transient effects when the driving the frequency is different from the resonant frequency. But still, it's not Doppler, the source is not moving, the oscillations, transient or not, are a displacement of the surface of the cone about the fixed point of it's suspension - which is fixed relative to the magnet, which is fixed relative to the listener.
Wouldn't it be nice if all of our speakers has such low resonant frequencies that we never had to worry about them.
Today I ordered in Tap Plastic a pair of 8"x30" panels made of double mirror plastic, with 16 1 1/8" holes in each. Let's experiment how microphone capsules will play music. If I connect 16 of 500 Ohm capsules in series I get 800 Ohm nominal impedance. I can drive them by 4P1L SRPPs with MOSFETs on top. The mirror is semi-transparent, so tubes should look nice behind the panels.
Stay tuned!
Actually the fact that it's a harmonic oscillator has nothing at all to do with doppler effect, I was merely pointing it out to correct the notion that somehow cone displacement is proportional to applied force.
Whether the suspension edges are fixed relative to the listener is also of no consequence, its the cone that is the source of the sound, and the cone is moving.
Think of it another way, by varying the cone excursion at low frequencies you are adding and subtracting a small relative time delay on each half cycle as the cone nears and retreats from the listener. (Since propagation speed through the air is finite, and in fact quite slow)
At the bass frequency itself this time delay is infinitesimally small relative to the physical wavelength and therefore represents an infinitesimal phase modulation of its own frequency - so small it would be impossible to measure, for all intents and purposes it doesn't exist.
However with a simultaneous tone of much higher frequency and much shorter wavelength the time delay variations represent a greater and greater phase shift until at a high enough frequency they are a significant percentage of a wavelength - in the example calculated by Linkwitz it works out that a 5mm peak excursion corresponds to a 10.3 degree peak phase shift at 2Khz.
If you were to electronically add a sinusoidally varying time delay to a 2Khz tone you would get exactly the same amount of phase modulation and frequency modulation side bands without an actual low frequency tone (or even a physical speaker) being present.
It's not rocket science
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Agreed, but it is how the cone moves that is important. Let me try to explain my thinking with a couple of graphs (attached). Each plot is designed to show the movement of the cone, the displacement of the cone from the magnet is 'x' and is shown on the vertical axis, the march of time is shown on the horizontal axis; both axes are linear.
A single sinusoidal frequency is applied to the voice coil. My drawing skills are a bit rough, the wiggles don't look like very good sine waves!
Plot (a) shows the cone movement under the application of this single input frequency. The period of oscillation is Tau (and the frequency is readily calculated from it in the usual way). The cone is otherwise stationary and the average position doesn't change over time - indicate by the horizontal line that cuts through the wiggly line and is parallel to the horizontal axis. I don't think there's any 'argument' over this.
Plot (b) shows what happens when we add a very low frequency signal to the initial high frequency signal. To keep it simply I've 'zoomed in' so that only a small part of the low frequency signal is visible, it shows as an almost linear ramp in the average position of the cone. This is indicated by the sloping line that cuts through the wiggly line showing the cone excursion slowly increasing over time. The wavelength of the low frequency signal is not indicated here since it's much longer than the size of the plot. The wiggly line shows the movement of the cone relative to the magnet, and hence to the listener. The cone moves and produces a high frequency sound signal with a wavelength of Tau. The listener will hear this high frequency sound unchanged compared with Plot (a) because the wavelength experienced by the listener is the same. Since there is no change in the frequency heard by the listener there is no Doppler shift.
Plot (c) shows what happens if we do Wavebourn's thought experiment and put a tweeter on the surface of the cone. We feed the cone with the same low frequency as before and we feed the tweeter with the high frequency signal. The high frequency signal has the same frequency as before. In this case the surface of the tweeter now moves relative to it's own magnet, not the magnet of the main river. The displacement of the surface of the tweeter relative to is own magnet will be a sinusoid. The tweeter magnet is fixed to the main cone, so the surface of the tweeter now moves in a sinusoid relative to the surface of the main cone. In my drawing, this means that the sloping line, representing the position of the main cone, becomes the horizontal axis for the wiggly line. The wavelength, Tau, remains the same for an imaginary listener sat on the main cone, but because the main cone moves at a low frequency, and the tweeter magnet along with it, the wavelength experienced by a listener who is stationary relative to the main cone's magnet will be different. This is shown in my diagram as "< Tau". The listener experiences a shorter wavelength and hence a higher frequency. This is Doppler shift.
For a single cone, where the movement is relative to the main magnet for both low and high frequencies Plot (b) describes the movement and hence sound experienced by the listener; there is no Doppler shift in the wavelength.
The same plots answer this question too.
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Deliberately misunderstanding my point. For any duration and resolution of measurement you wish to specify, I can specify a very low frequency AC waveform that will appear indistinguishable from DC. For shorthand, we could just call it "DC".
As I mentioned a few posts ago, a 'speaker' can be a small disc attached to a plunger on a linear motor a mile long. Just because it isn't a practical speaker doesn't mean that it suddenly becomes inapplicable for thinking about the phenomenon of Doppler shift in speakers - if it exists. The bass note can be 'DC' to all intents and purposes. The plunger can continue receding or advancing in one direction for minutes or hundreds of yards at a time - that's the power of a thought experiment! The question is: why would you not measure Doppler shift on a 10kHz tone as the disc receded away from you continuously at 1 m/s? Would the 'correct' drive signal for a mix of bass and 10 kHz signals result in a compensating (continuous phase/) frequency shift of the 10 kHz tone, compared to the tweeter-glued-to-a-woofer scenario? If so, how should the two differing drive signals be computed? To me, they would both seem to distil down to the same formula, so Doppler would, indeed be experienced in both cases...
Intuitively, I am beginning to think that the only elegant solution is that theoretically there should be no Doppler shift with a 'perfect' full range speaker. Is it simply that the low frequencies reproduced by the cone (including DC) affect the medium through which the 10kHz tone is propagating? In other words, attach a tweeter to a woofer cone (of arbitrarily large - probably infinite - size) and you don't have Doppler shift. However, replace the woofer cone with wire mesh, and you do have Doppler, even though the attached tweeter is moving through space identically in both cases. The Doppler is not caused just by displacement of the tweeter, but by the lack of low frequency air 'movement' to compensate for the displacement of the tweeter. This conjecture is beyond my knowledge of physics however: would it be that the speed of sound was varying with air pressure or some other property of the low frequency movement of the air? Would this compensation only work perfectly in an infinitely-sized listening room? Anyway, the implication would be that your cone's low frequency displacement should be limited commensurate with its abilities to 'move' air at low frequencies (they usually are anyway), so that my examples of the mile long linear motor or the wire mesh cone would certainly be producing 'unnecessary' levels of Doppler shift.
Or am I barking completely up the wrong tree?
The nature of doppler effect is the stretching and compressing of steady state soundwaves due to the movement of the transducer in relation to the listener.
the nature of the transducer is immaterial, a screaming baby or a diamond dome HLCD. The nature of the movement is immaterial, back and forth or one direction, towards or away. The nature of the medium is immaterial, water or air(i prefer breathing air myself).
Its kinda crazy how this thread has taken off. I just wondered if given similar enough freuency respons e would we as time based creatures prefer a single point source to a multi driver setup due to phase errors derived due to multiple points of radiation?
I do wonder if the benefit of a line array is due to the swamping of the ear brain by multiple sources so it quits processing them as separate sources and averages their output. Kind of like you only feel your shirt for a few seconds after you put it on before you forget about it.
the nature of the transducer is immaterial, a screaming baby or a diamond dome HLCD. The nature of the movement is immaterial, back and forth or one direction, towards or away. The nature of the medium is immaterial, water or air(i prefer breathing air myself).
Its kinda crazy how this thread has taken off. I just wondered if given similar enough freuency respons e would we as time based creatures prefer a single point source to a multi driver setup due to phase errors derived due to multiple points of radiation?
I do wonder if the benefit of a line array is due to the swamping of the ear brain by multiple sources so it quits processing them as separate sources and averages their output. Kind of like you only feel your shirt for a few seconds after you put it on before you forget about it.
It's all very simple.
But what if the nature of the medium changes as the source is displaced? Or the medium itself 'moves' because of the displacement of the source?
How can there not be doppler shift? You move a sound source you get doppler shift. Its thats simple. If your cone is a 1khz source and you move it, you will change the pitch. And its the cone that creates the pressure wave not the magnet , not the magnetic field nor anything else. Move that cone and you will get a doppler effect. (modulation is still caused by dopplering, its just not steady steady state). How audible this effect is I have no idea, but the effect is there. Try it. Listen to a 200hz tone, then listen to a 200hz tone mixed with 30hz. (on a woofer that can produce 30 hz) There are many factors, but the more the 30hz moves the cone the more audible the doppler will be.
As far as mics dopllering, only the dynamics and ribbons will do this (as stated earlier very little), the pressure mics (including the condensers) will not.
As far as speaker arrays , they behave differently near/far field, and the near field will be a lot larger than 2 way speakers. And PA arrays use very directional speakers at a great distance, so this is not a fair comparison.
As far as mics dopllering, only the dynamics and ribbons will do this (as stated earlier very little), the pressure mics (including the condensers) will not.
As far as speaker arrays , they behave differently near/far field, and the near field will be a lot larger than 2 way speakers. And PA arrays use very directional speakers at a great distance, so this is not a fair comparison.
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