A 555 astable has no clock of its own. The RC is the clock.
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The NE555 has three comparators worth of analog logic inside an 8-pin chip and no oscillator at all. Every timing interval in an astable or a monostable circuit comes entirely from the resistor and capacitor wired around it. That is worth saying plainly, because it means the chip's accuracy is only ever as good as the RC network's, and the formula below is the whole of the math.
In the circuit above, R1 is 1 kilohm, R2 is 4.7 kilohm and the capacitor is 100 nanofarad. The astable frequency is f = 1.44 / ((R1 + 2 x R2) x C). Put the numbers in: 1.44 / ((1000 + 9400) x 100e-9), which is 1.44 divided by about 1.04 milliseconds worth of RC, giving roughly 1.4 kilohertz. That is the pitch you hear from the piezo, and it is a real result of that R1, that R2 and that capacitor, not a canned tone.
Inside the chip, three 5 kilohm resistors from the supply to ground set two comparator trip points, at one third and two thirds of the supply. The capacitor charges through R1 and R2 toward the supply; when it crosses the upper third the chip's internal flip-flop flips and starts discharging it through R2 alone, back down past the lower third, where it flips again. Each half of that cycle takes a slightly different time because charging goes through both resistors and discharging only through one, which is why an astable's duty cycle is never quite 50 percent unless the circuit is built specifically to make it so.
None of this happens in zero time. The comparator-to-pin path here carries a 100 nanosecond delay, taken from the chip's own datasheet. The capacitor and the two timing resistors are solved together as one matrix, and the comparators tell the solver where their trip points are, so the step lands on the crossing instead of stepping over it and the period comes out within a twentieth of a percent of the formula from 1 kilohm to 100 kilohm. The chip's own transistors are not modeled, only its behavior. Change R2 or the capacitor in the properties panel while the astable runs and the pitch moves by the amount the formula predicts, not merely in the right direction.
RESET is wired straight to the supply here because nothing in this circuit ever needs to stop the oscillator. Change it to a switch and the astable can be gated on and off, which is the natural next thing to try once the basic timing makes sense.
Want the step-by-step version? The lesson "Timing with a 555" walks through this with checkpoints.
Open the lessonBuild this for real
Open the editor, change a value and watch the number move with it. Nothing to install, and no account needed.