Op-Amp Comparator precision voltage
Do you even need +15V to -15V output???

Power on the speaker is ~Vpeak^2/R, so for an 8 ohm coil this system will blast out 15^2/8 ~= 28 Watts, which is pretty loud.  Also placing DC current through a speaker is bad for it.

If you wanna stick with this design: you're going to need a Comparator with Rail-Rail operation, and even then that only gets you to Vdd-0.3V and Vss+0.3V .  Check to see if this suits your needs.  Since you are also driving a speaker, use Ohm's law on the speaker impedance to figure out how much current you're gonna need.  An 8 ohm speaker will need at least a 2 Amp power supply for both +15 V and -15V. Best bet is to drive the system with +-18V 3A Rails. Find a comparator that can handle +-15V outputs, and get an output buffer that can handle 2 Amps both ways.