magnets detuning strings

[aquin43]

I know that this topic has been visited repeatedly, but I couldn't find a thread that came to a definite conclusion.

How does a pickup detune a string and cause beating? Is this a plausible argument:

Apply a constant sideways force to the centre of a string using a long effectively massless spring. The string is bent out of true so the tension increases and the vibration frequency rises. The vibration modes of the string are otherwise unaffected by the massless spring.

Replace the spring with a close magnet pole attracting the string. For small amplitude vibrations, the effect is essentially the same. There is one difference. The attraction of the magnet varies with distance, with a large square law component. So, the loading on the string will vary throughout each cycle of vibration - more at larger amplitudes.

The velocity of longitudinal waves in the string is governed by the speed of sound in the material and is much higher than the velocity of the transverse waves. This means that the changes in tension due to the loading propagate along the string virtually instantaneously in terms of the frequencies of the transverse waves. The whole string is affected, not just the loading point.

We thus have a string in which the overall tension is modulated by its own vibration.

However, this is only in the plane perpendicular to the face of the magnet. For motion across the face of the magnet, the attractive force varies much less with displacement. The modulation in this plane is much smaller.

So, we have a string where the vibrations in two planes can differ. For a small amplitude of vibration both modes will have the same frequency, but at larger amplitudes the frequency of the perpendicular mode will rise because the square law component of the attraction will raise the average tension.

We now have a string with motion resolvable into two modes of vibration of slightly different frequencies but coupled via the tension modulation.

Arthur

[antigua]

The magnet pull upon the strings makes differences that are observable in both the waveform and in an FFT analysis. The difference varies not only with strength, but where along the string the pull is occurring. I think it's an important finding because most of what Im interested in doing is separating fact and fiction when it comes to what pickups can and can't do, and it's demonstrable that magnetic strength influences the timbre, if only subtly.  

I tried an experiment where I measured the output from the neck pickup, while raising the neck and bridge pickups separately, and then vice versa, and it appeared that the biggest differences in harmonic levels were observed when the same pickup that is selected is the pickup being raised or lowered. For example, raising the bridge pickup caused and uniform increase in harmonics, but that difference was more apparent when the bridge pickup was also selected for the output. So even though magnetic pull effects the string in a global manner, it's easy to see why its something that has come to be associated with the particular pickup, as opposed to the guitar string as a whole.  

I have another thread talking about whether a magnet should be modeled as a spring or a damper. You said a spring, but the thing about a spring is that it receives and releases energy, where as magnetic pull doesn't cause a release of energy. On the other hand, a damper usually dissipates energy as heat within the damping agent itself, and Im not really sure that's happening. When the magnetic domains re-orient in the moving magnetic field, there might be some heat generated, but I'm not sure if those moving domains manifest as a form of mechanical resistance.

[aquin43]

I only brought in the massless spring as a source of a constant force in the first paragraph.

In fact, a magnetic pull can act in a similar manner to a spring. There will be a continual change in the potential energy as the string moves with energy flowing into and out of the magnetic field. Only the hysteresis of the magnetisation curve of the magnet material will cause losses and I would wager that those losses are negligible compared with the total energy in the string movement.

Consider the magnet pulling on the string. If the string moves closer, the pull increases. If it moves further away, the pull decreases. So the attraction can be modelled as a spring superimposed upon a constant force. The dynamic equations governing the oscillation will factor out the constant force leaving the magnet acting as a spring (albeit an non-linear one)

What I was proposing was a mechanism whereby the equation of motion of the string would become non-linear due to the  magnet varying the tension through the cycle of oscillation and also that the non-linearity could produce more than one resonant frequency in the string at the same time. I would expect that the modes of vibration with slightly different frequencies would interchange energy, each dominating in turn.

One would also expect the modified harmonics to be most noticeable in the pickup that is causing the effect because the proximity will also increase the variation of the magnetisation of the string so there will be a double effect on that pickup.

This proximity effect will be perhaps the prime reason for the change in tonality as the pickup distance is varied, even before any obvious modulation is produced. When the pickup is far away, the string magnetisation will vary little during the cycle. When it is close, there will be a strong square law modulation of the magnetisation. This will cause distortion in the string output but no intermodulation between strings because they are too far apart to affect each others  magnetisation.

Arthur

[antigua]

If you have two magnets opposing, then there is stored energy in that the magnets want to repel, and will return any energy that is put into forcing the together, but if the magnets are attracting, as is the case with a pickup and steel string, the energy is lost when the magnets come  together, and the magnets will not separate again until energy is put back in. The guitar string itself acts as a spring in that it stores the energy of the pluck, and releases that energy over a period of time, but because this storage and release happens with or without a magnetic pickup present, as with a plain Jane acoustic guitar, I'm reluctant to say the magnetic pull is contributing to a spring analogy, rather than somehow impeding it. 

I think you might be right that there is added damping in the form of magnetic hysterisis, but also if tension is added to the string, there might be more heat loss in the guitar string itself, and you're right that these losses are probably laughably small, and so even if the magnet represents damping, it has no practical damping effect. I think this is an important issue to work out because it's common belief among guitarists that strong magnetic pull reduces sustain. If sustain is reduced, I dont think it's due to damping, but maybe because the ability for the string to sympathetically vibrate in a uniform manner is reduced, or something like that. 

I did an experiment showing wolftones emerge with strong string pull: guitarnuts2.proboards.com/thread/8002/analyzing-wolf-tone-effect-spectrogram  At first the pitch drops, but as the pull becomes stronger, two distinct pitches occur, and beating occurs, and at that point the duration of decay (or sustain) is reduced. 

[aquin43]

I think that the simplest explanation of why magnetic attraction can't act directly as a damper is that the force has no time component. By placing the string near the magnet you create a system with potential energy. Neglecting the string tension, if you pull the string further from the magnet you have to do work against the attractive force. The string-magnet system is now in a higher potential energy state, storing the work you did. Return the string to its original position and, on the way the magnet is assisting you - it is doing work, the energy for which comes from reducing the potential energy to its original value.,

Similarly for moving the string towards the magnet. The lowest energy state of the magnet-string system is with the string in contact with the magnet. To get it out of this state you have to do work against the attractive force, which then becomes stored as potential energy. In the normal case, the string tension is holding the string-magnet system in a higher energy state by preventing the string from falling onto the magnet.

An important part of this is that the equation for the force from the magnet is single valued - one force for any position - and independent of time, so if you return to position x you get force y and it doesn't matter how or when you do it. Such a system can store and return energy, but will not dissipate it.

Any perceived damping must come from the change in the way the string oscillates, as you suggest.

There are, though, ways in which the string motion could be damped. Hysteresis and eddy currents in the magnet introduce a time dependence in the attractive force which could dissipate energy. The speculation so far is that these can be neglected.

I note that you say that the string frequency falls with increasing attraction until the split into beating notes. I had expected a rise, and so must think that through more carefully.

Arthur

[antigua]

I can believe the magnet isn't acting as either a damper nor a string, because it doesn't seem to meet the qualifications of either (at least not at a macroscopic level). Maybe it's more as though the shape of the string itself changes temporarily, changing and unchanging as it gets nearer and further from the magnet(s).