Well I forgot there was a metal part inside the coil (I've never built any woofers only wanged em) but my original statement of the coil generating a sinusoidal voltage was based on the other coil being energized (say by an amplifier) and causing the entire assembly to move through the magnetic field (thus generating a sinusoidal voltage on the other coil).
If you're just referring to the current being transferred through that core, how will there be any energy transfer without the assembly moving? If the assembly isn't moving then your either not supply power to main coil or your supplying it with DC, neither of which are relevant cases.
Also, I know you think your helping but your coming off kind of condescending. I don't mind being wrong but don't speak to me like a child.