Electronic – Why doesn’t this transistor circuit work as expected

I was able to simulate this circuit and play around with it a bit. The relationship between the voltage of the solar cell, the 330k resistor and the 10nF cap sets the operating frequency of the circuit. The difficulty in inverting this relationship is that the condition in which you want highest frequency (low light) also corresponds to the condition where VCC is lowest. Unless you can introduce an additional voltage supply independent of the solar cell, I don't see how you can achieve what you want. Sorry...

CircuitLab allows you to simulate this:

^{simulate this circuit – Schematic created using CircuitLab}

Open the circuit, click on "simulate," and figure out how it works yourself! Note that I had to simulate the inductance of the speaker (important in this circuit) by inserting a series inductor, as CircuitLab didn't include this in the speaker model.

Separately, the reason the capacitor is connected to the speaker's "top" terminal, rather than ground, is that it needs to see the voltage drop across the speaker, which fluctuates with both how the speaker conducts, and how Q2 conducts; this is what keeps the oscillation going. If the capacitor was connected directly to ground, there would be a single click, and then it would be silent.

Specifically, when Q2 is open, the voltage across C1 will drop to 0 (it will discharge.) But, as C1 discharges, it turns from an isolator to a conductor (a discharged capacitor works a bit like a wire; a charged capacitor works a bit like an isolator.)