Limiting the Q3 collector current by starving its base is called dangle-biasing, and is *very* unreliable. The beta of a transistor changes with temperature, atmospheric pressure, collector current, base current, and just about everything except the phase of the moon.
Thank you for discussing this circuit. I built it many years ago and it is still working in these days.
Now, I wonder why I added the 2 LEDs. Their current is too low to let them emit a practical visible light when Q2 is off.
Here, when the mains is on, the V(CC) limit is about 54V. When Q2 is off, (mains is off) and Q3 starts to trun on, Q3 Vce is relatively high which lets its current gain, Ic/Ib, be high too. In case of BC337, this gain is about 200-400. Therefore, for a 3 mA collector current, the base current needs 15 uA. And the base voltage = Vbe + Ie*R9 = 0.6 + 3*0.220 = 1.26V.
At this moment, V(CC) should be (15uA*1megaR + 1.26) = 16.26 V which is much lower than the starting 54V. This means, the margin is rather big.
For instance, the collector current is distributed between C3 and the buzzer. The charged C3, besides supplying the pulsing currents of the buzzer, keeps the buzzer sounding a bit more, though not with a continuous sound.
You already have R9 in there, which will limit the buzzer current. I'm curious - why is it in the emitter rather than the collector?
In real life, a new final circuit is the end fruit of many changes, if not the fruit after trying several different methods.
R9, at the emitter, was supposed to reduce the effects of the temperature sensitivity of the current gain and Vbe. But in this final circuit in which the two LEDs have no practical role (they can be removed) and a wide range of gain is tolerable, R9 could be moved to be at the collector instead of being at the emitter.