Hall effect chips are simmetrical devices: given a small current flowing through a diagonal of the square chip, the perpendicular component of a magnetic field to the chip die will cause a voltage to appear at the other diagonal, the intensity and polarity of the voltage being proportional to the intensity and polarity of the magnetic field.
I tested the circuit on a protoboard, no solder job, no PCB. The components are easy to find and the thing can be assembled in a very short time.
Step 1: The circuit
The differential amplifier is necessary because the VCO needs a voltage referenced to ground. It does not actually amplify the signal, simply adapt the voltage reference.
The Hall sensor is courtesy of a floppy disk drive while the operational amplifier comes from one of my spare parts boxes. It could be replaced by almost any op amp suitable for single supply. The VCO is part of a 74HC4046 chip. This one is a PLL chip, a component used to generate frequencies with reference a stable and precise reference, typically a crystal quartz. I just needed the oscillator which is good enough for the purposes.
The VCO output then goes to a piezo buzzer.
The Hall effect sensor I placed on a 2x2 piece of perfboard, this makes it easier to handle.
The chip is symmetric, this means you can connect it with the single requirement that the pins going to the differential amplifier be on a diagonal and the supply on the other one.
There isn't really much more to say. No, wait, should you find the pitch too high and annoying, you can make the capacitor 100nF.
OK, that's really all for now.