I built a similar beeper from the oscillator that can be made from two logic inverters, a resistor, and capacitor.
The inverter IC can be 4049 or 4069. Six inverters are on one chip. I forget whether they work on 3V.
I used two oscillators, (a) one at high frequency, (b) the other low.
The high F one drives a piezo beeper.
The low F oscillator is the on-off device. Its output alternately allows and prevents operation of the second oscillator.
To do this, the output of the first oscillator goes through a diode and resistor, to the next oscillator (the high F).