This looks like an over complicated way of doing it.
This simplest is to use an LM311 and a pulsed piezo buzzer.
If you must build your own oscillator, then I'd opt for a quad LM339, configure one as a low frequency oscillator, the second as an audio frequency oscillator and the third as a comparator.
I don't see any reason why this should require more than one IC plus a voltage reference.