Notes: 100nF (first example) and 10nF (second example w/ speaker) capacitors are used. Unfortunately, there is also one major flaw in this first OP set-up (100 Ohm resistor instead of 1 kOhm resistor, i.e. 1.1 kOhm and not 2 kOhm for R2).
As with any oscillator, no input is needed. It swings by itself.
A 10 nF capacitor would lead to a tenfold increase of the frequency.
The first OP stage is an integrator (note: negative feedback loop), the second a non-inverting Schmitt trigger (note: positive feedback loop).
The wave is triangle shaped on the integrator output (IC pin 1) because the capacitor is forced to charge linearly: the current through resistor R1 is constant and the input of the OP Amp draws (virtually) no current.
The gradient x (V/ms) is calculated by the following formula (U_s would be 9V here):
R2 and R3 determine the voltage thresholds (therefore the oscillator frequency) of the Schmitt trigger.
No reset switch for the integrator is needed, for it is part of a larger device i.e. oscillator.
There has to be a plus and a minus voltage (ideally symmetrical) to supply the whole thing. This isn't always readily available (though you can just use two 9V battery blocks).
But one can built up a power supply with an OP Amp too. Below you see a quick&dirty set-up with a UA741CN OP Amp (active voltage divider) and a couple of transistors that I scrapped from electronic waste (this design has some problems, therefore I don't share the schematic).
An unsymmetrical supply voltage will lead to an unsymmetrical triangle-wave signal; the oscillator won't swing at all if it is too skewed.
Not yet decided for this project. The oscillator could be part of a sound generator/synthesizer.
A triangle signal generates a very distinctive, not too unpleasant sound (triangle signals consists solely of odd harmonics: 1st, 3rd, 5th, etc.).