Solenoid Question

["xeno_tropic" <xeno_tropic@xxxxxxxxx>]

Hello. I have a question. I do not need to know about solenoids 
specifically, as in actuators. I am building variations of a device 
which must generate a time-varying magnetic field at audio 
frequencies. 
The current source is the audio output jack of a CD player.
I wound a small coil around a ferrite core, using fine magnet wire 
from Radio Shack, two layers, tightly wound both leads at one end. 
Now I wish to make many of the devices, and wish to avoid winding all 
those coils. I would like to purchase ready-made ferrite core coils.
My question is, what factors might affect:

1. The strength of the magnetic field
2. The signal characteristics as to reproducing it faithfully,
like the first coil I made

Is wire diameter, number of turns, diameter or length of core 
critical? It is very important that I get this right.
Thanks in advance for your help.
James Roberts