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It seems obvious to me that the principal behind a standard electric guitar could be reversed, so that electrical signals passed through the coils in the pickups could induce a vibration in the string and thus cause it to emit a sound. Would simply driving the resonant frequency of the string through the pickup be adequate to produce sound like this?

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    $\begingroup$ Speaker coils indicate the process can work in general. However, coils as sensors are designed to different criteria than coils as drivers. $\endgroup$ – Jon Custer Oct 1 '19 at 21:01
  • $\begingroup$ A science equipment company, PASCO, used to sell a set of coils, one a driver and the other a detector. Both were iron/steel cores wrapped in copper wire. The detector had more turns of wire to make it more sensitive, but their basic constructions were the same. $\endgroup$ – Bill N Oct 17 '19 at 19:29
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There is something which does exactly this- it is a small battery-powered device called an E-BOW which the guitarist holds in their right hand near the strings. It contains a pickup coil, an amplifier, and a drive coil. When the pickup coil detects string vibrations, the amplifier makes the signal more powerful and sends it to the drive coil, which forces the string to vibrate more strongly at its original frequency. By driving the string in this manner, the E-Bow lets guitarist hold the note of their choice forever without physically plucking that string. The guitarist for the band Tom Petty and the Heartbreakers used one for the guitar solo in the song "Breakdown", from their first album.

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  • $\begingroup$ why the downvote??? $\endgroup$ – niels nielsen Oct 1 '19 at 15:59
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My understanding of the detection vs driving is as follows:

Firstly, as Jon Custer has mentioned in the comment above, the detection coils are designed for detection. They are very sensitive, but unlikely to drive a string, because they are not suited to supplying the required intensity of varying magnetic field required.

Secondly, the vibration frequency $f_1$ of a string is according to the following equation:

$$f_1 = \frac{\sqrt\frac{T}{m/L}}{2L}$$

by which vibrational frequency is determined by its effective length $L$ (for a given cross sectional area and string material, which determine the mass $m$ per unit length $L$), which also affects tension $T$ in the string. These two are the short term determinants of the fundamental vibration frequency of a string.

There is no need to drive the string at a certain frequency, if it is plucked or hammered, it will vibrate at a frequency determined by its effective length.

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