# Creating sympathetic resonance in a guitar string with an electromagnet

I have an idea for a potential new type of reverb and I wanted to know if it was possible/practical.

The idea is to have an electromagnet in the middle of a guitar string(s) which will hopefully cause the strings to vibrate. The vibrations would then be captured by a pickup at some other harmonic point along the string.

I suppose that the tautness of the string would determine the necessary strength of the electromagnet so I was thinking that the strings would need to be tuned octaves below my desired resonant frequencies. This is because it seems like it would be easier to cause the string to vibrate at a frequency further up the harmonic series from its fundamental frequency due to the smaller distance that the string would need to travel...

I suppose this question isn't very clear. Ummm... Questions:

1. Does the strength of the magnetic force exerted on the strings depend on voltage or amperage, or both?
2. Is it feasible with 9V and 100mW?
3. How would I even begin to calculate the amount of electromagnetic energy required to start a string vibrating?
4. Is it more feasible to have an inductor and a permanent magnet and physically connect it to the string, i.e., take apart a speaker and tie the cone to a string?
5. If a body is made to resonate at harmonic frequencies will these smaller vibrations eventually combine to cause the body to vibrate at its fundamental, e.g., if the string is tuned to C3 and I create vibrations at C4, C5, and G5, will it eventually start vibrating at C3? i.e., do harmonics work in reverse?

An electromagnet will only cause a guitar string to vibrate if the current through the magnet is varied at 1/2 of a natural frequency of the guitar string. The force will depend on the current, but also on the distance between the string and the electromagnet and on the shape of the end of the electromagnet which is closest to the string. The fundamental natural frequency, of course, depends on the mass density, the tension, and the length of the string; and the harmonics are the frequencies obtained when the string vibrates in sections of 1/2, 1/3, 1/4 ... of the string's length.

The required amperage will depend on how fast energy is lost in the form of sound and in energy absorbed by the guitar body, so it will be difficult to calculate. A crude estimate of required power could be made by, e.g., finding how much power you would need to feed to a speaker to get the sound amplitude you want to get from the (un-amplified) guitar. However, if the guitar is amplified, the amount of power needed by your reverb itself should be quite small: the amplifier would provide the sound amplitude you want.

Attaching anything to the string will alter its sound dramatically, usually making the tone fuzzy; and the effect will be different for different notes, so you probably won't like the result if you attach any part of a speaker to the string.

In my experience, with a good-quality string and a decent guitar, if I induce a higher harmonic in the string (e.g., by touching the string precisely in the middle and plucking it 1/4 of the way from one end) it does not decay to lower harmonics. That harmonic just slowly dies out as the string vibrates.

A way you could test your idea is to get a microphone, amplifier, and speaker. Use the microphone to pick up the sound from a vibrating string on your guitar. Take the coil from the speaker to make an electromagnet, and place it close to your string. Use the amplifier to feed the amplified signal from the microphone to the electromagnet. Pluck the string and see what happens. You may find that you need to modify the electromagnet dramatically to get it to couple efficiently with the guitar string.

• Also when the current is a 1/4 of the natural frequency. It is like pushing a swing every other time. It adds energy to the fundamental mode. – Pieter May 27 '18 at 20:51
• True -- and 1/4 of each of the harmonic frequencies, too. – S. McGrew May 27 '18 at 21:00

Strings for electric guitars are magnetic, so an electromagnet will work fine. But there is a complication, that the electromagnet will pull the string twice per period of the AC signal: when the current is large positive and when it is large negative.

I have been using driver coils from Pasco. Resistivity of these is about 10 ohm, current up to 500 mA. But many other designs should work. At resonance, the required force is small.

• What about the mathematics required to calculate how much the string would move given a specific power applied? – Tim May 26 '18 at 22:21
• Far enough below resonance, one can make the static approximation: if the force is one promille of the tension of the string, the amplitude will be a deviation of about one milliradian from equilibrium. That would need an unrealistically strong electromagnet. But at the narrow resonance, the necessary force is reduced by the Q-factor (about $10^3$). – Pieter May 27 '18 at 0:18