Some references have been mentioned in the text and I thought that it would be a lot easier to provide the the pdf files instead of just having a list of references as is usual in scientific publications. I have already warned the readers, quite a bit of the content here is theory that can be difficult to follow and it would take a higher university degree to understand. In some cases, however, it can be quite instructive to look at some of the figures.
Even in this case, some of the information in these publications is wrong or misleading. Sometimes the information is repeated myths. I have tried to correct all these mistakes in the pages on this website.
This is reference (1). A book that covers a wide range of material related to guitar, specifically electric guitar. This is what I would call a PhD level treatment of the material, but I think Chapter 2: Vibes should interest a lot of readers. I have only briefly covered this, because the page was mainly about guitar pickups, it is never the less very interesting for the reason that everything starts with a vibrating string. The book is titled: “The Science of the Electric Guitar and Electronics”.
The following reference is what is referred to as (2) in the text. It is kind of brief and can be hard to follow. It is referred to in (1) so it is included here for completing the information. The paper is developing a theory for calculation the pickup output based on the string movement, but it concludes that the equation has no mathematical solution, which is not unusual, so it is solved numerically. The solution is just reported, not shown in detail, something that would have been interesting.
Next is a Masters degree thesis, it is kind of date from 1994 or so. It does contain some myths that have been debunked, I have pointed to these myths elsewhere on this site and done my debunking. It was included to give an easier to read version of the Vibes, also it has been referred to a “Jungmann” on the Electronics page where I make use of some of his experimental data.
I have included the next one because it has been considered to use his findings on the pickup page, especially the equation numbered (13). This equation is for calculating the pickup output for small string excursions and for a pure sinusoidal input. I have been working on developing it to a point where it is using some of the data from my own setups, it is still a work in progress. It shows a complete solution to the induced pickup voltage and a simpler version based on some assumptions about string excursion and string height. The solution only leaves the fundamental and 2nd harmonic, so it is a solution for when the higher harmonics have died out. The paper does present some graphs that are in agreement with (2).
I have a couple more that has not been called out as references yet, they will be added if anything new should come up.