Light Reading

[rjb]

I recently googled upon this article by a Princeton physics prof & thought some folks here might find it interesting.

Although my vector calculus is "a bit rusty", I do like to look at the pictures. And the reference list has links to pdfs of some seminal patents.

Enjoy:

http://www.physics.princeton.edu/~mc...les/guitar.pdf

-rb

[tedmich]

nice post, it ref. a recent modeling article which is discussed here:
https://docs.google.com/leaf?id=1tq0...v00ib&hl=en_US

also
http://online.physics.uiuc.edu/cours...asurements.pdf

http://online.physics.uiuc.edu/cours...lk_1-29-10.pdf

http://sem-proceedings.com/25i/sem.o...ar-Pickups.pdf

http://www.nelsonresearchinc.com/Wor...r%20Pickup.ppt

[Corona Blue]

Thanks for this... great stuff!!

Thus, the electric guitar pickup does not generate an accurate reproduction of the direct
acoustic sound of the guitar, but rather creates a more complex waveform, leading to a
distinct musical esthetic.

[Mike Sulzer]

I recently googled upon this article by a Princeton physics prof & thought some folks here might find it interesting.

Although my vector calculus is "a bit rusty", I do like to look at the pictures. And the reference list has links to pdfs of some seminal patents.

Enjoy:

http://www.physics.princeton.edu/~mcdonald/examples/guitar.pdf

-rb

Well, that is a complicated analysis, but he did correctly predict that string motion parallel to the face of the guitar is a frequency doubler. I have not seen that in so many places. However, it has always seemed likely that this doubling behavior is not that significant. He shows that it is suppressed relative to the output from vibration perpendicular to the face of the guitar when the string is close to the pickup. The example he shows in the figure, where the doubling does have a significant effect, is for a 5mm spacing. (That is half a centimeter.) This is kind of large; 3/32"(2.4mm) is more typical; so I think that waveform is not typical. But there will be some doubling present, and thus some tendency to produce triangular shaped waveforms.

[Mike Sulzer]

Some more comments on this solution:

Step 1. is to find the magnetic field produced by the string when it sits in the constant field of the permanent magnet. This is the result of magnetizing (temporarily) the magnetic material of the string.

Step 2. consists of moving the string (and thus the field it produces) and so changing the magnetic flux through the coil. The law of magnetic induction determines the voltage induced around the coil.

There is no mention of magnetic reluctance because it does not enter into the solution.

It has been discussed before how the inductance of a coil increases when a magnetic core is used. The increase can be very large when a closed core is used so you can think of the magnetic flux circulating. When an open core is used, the increase is smaller, and increasing the permeability of the core material beyond a few times that of air makes little difference. This solution shows the same effect for the string: the permeability of the string material makes no significant difference once it is larger than a few times. So the magnetic operation of the pickup is not dependent on the material of the string for a wide range of ferromagnetic materials.

Concerning the frequency doubling mentioned in a previous post: The author of the paper has made some simple assumptions regarding the nature of the coil. I believe that it is a single layer with either no core or one with low permeability. The actual coil and core used will influence the amount of doubling from string motion parallel to the face of the guitar. But the basic behavior should be similar. The doubling goes away very quickly as the string height is reduced because of the third power term involving h and w in the denominator of the approximate form of equation 13 for the voltage. And power is proportional to the square of voltage.

[David Schwab]

Well, that is a complicated analysis, but he did correctly predict that string motion parallel to the face of the guitar is a frequency doubler. I have not seen that in so many places. However, it has always seemed likely that this doubling behavior is not that significant. He shows that it is suppressed relative to the output from vibration perpendicular to the face of the guitar when the string is close to the pickup. The example he shows in the figure, where the doubling does have a significant effect, is for a 5mm spacing. (That is half a centimeter.) This is kind of large; 3/32"(2.4mm) is more typical; so I think that waveform is not typical. But there will be some doubling present, and thus some tendency to produce triangular shaped waveforms.

I used to find that on bass, if I plug the two pickups out-of-phase, and then played through a fuzz above the 12th fret, that I got a nice natural octave doubling effect. Probably due to this. The out-of-phase pickups reduced the low end enough to hear it with the distortion adding harmonics.