Hello.
I am currently researching alternative ways to pickup a vibration in a ferromagnetic and/or conductive string, mainly has a thought exercise.
Lastly, I am investigating hall effect sensors for the following two setups after some thought :

1. A guitar string (less conductive but with better vibrational/strength characteristics) with 0.5mm diameter would be subject to a fairly large DC current. under low voltage. (1A to 5A), a couple of volts.
   
2. A pair of Hall effect sensors (3503) would be placed at 4 to 5 mm to the string, perpendicular to the string, at both sides of the string.
3. Since the string creates a static magnetic field from the current it passes, the vibration makes the field oscillate. It is picked up by the hall effect sensor
4. The magnetic field intensity would be quite low, by using Ampere Law, it would be in the 60 to 100µT range.
5. The amplitude of voltage variation range at the hall sensor would be proportional to the string oscillation travel.

Since i never played with Hall effect sensors and datasheets do not give all information, I wonder if it would work practically, and I have some questions :

1. Is the 3503 sensor sensitive enough / low noise enough at the µT range?
   
2. bandwidth is 23 KHz as per datasheet, so audio transcription should be OK ?
3. What kind of preamp setup should i use ? I wonder if a phono preamp without RIAA equalization could be ok, I assume delta voltage would be in the µV range.

I wonder if I got it right...
The other setup would not use any current but a little (1.5 mm OD) neodymium magnet bead/toroid passing the cable in proximity to the sensors. It would probably dampen vibration a little but would probablybe easier to build and with way larger output at the sensor.

 

I think it would be better to try with a biasing magnet.
Experiment and see.

 

My gut feeling is that @dendad is right about the biasing magnet as opposed to running current through the string. Just a hunch though.

I will say that at the tiny signal levels you're planning to work with, there are a number of obstacles to overcome. A more sensitive sensor might be helpful. I've worked extensively with the Honeywell SS495 and have had nothing but good experiences with it. I'm not using it in audio applications, but it looks suitable. Frequency response is down less than 1dB at 20kHz with 5V supply, and perfectly flat to 20kHz with 10V supply. Sensitivity is 3.125mV/Gauss, quite a bit higher than the 1.3mV/Gauss for your sensor. Obviously it'll still need a lot of amplification, so maybe the sensitivity doesn't matter, but my gut feeling is that starting with higher sensitivity improves your odds of success. The SS494 has higher sensitivity (5mv/Gauss) and I believe the other specs are identical.

A sensor with even better sensitivity is the Hamlin programmable-gain analog sensor. It comes in a nice housing that's easy to mount, and boasts a default sensitivity of 11mV/Gauss. Unfortunately, I can't seem to find any info on frequency response.

Anyway, the other thing to watch for is that the earth's magnetic field is almost as strong as the fields you plan to work with, meaning if you rotate the sensor suddenly, the earth's magnetic field will register as a sound!!! So, you'll need to be thoughtful about implementing appropriate band-pass filters on this signal.

That's all I've got for now. Sounds like an interesting project. Have fun!