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I've been analyzing this circuit and so far I think it divides in two separate oscillators, but I still don't have a clear idea on how this two work together.

I'm leaving a picture of the circuit, any help will be appreciate it

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You can see two multivibrators, so you've got an idea of what this circuit can do. Step back a bit, and look at some key components.

The loudspeaker is connected to the left half, and looking to the right of the speaker, we don't see any interconnections, except for the wire that runs to VR1. So the two halves work almost independently.

Next, we look at the two ends of VR1. On the right side, it is connected to the emitter of Q4. This is a low impedance output, so this tells us the right side isn't going to be affected by this interconnection. On the left side, it is connected directly to the base resistors of the left-hand oscillator. From this, we infer that the signal from the right will affect the left.

A little intuition suggests that two oscillators running near the same frequency, mixed together, would produce a jumble of sound, not very useful or pleasing. So, we guess that the right-hand oscillator runs at a slow frequency, and changes the tone back and forth for the left-hand oscillator. We can verify this by looking at the capacitor values that cross connect the bases of each oscillator. Bigger capacitors mean lower frequencies.

SW1 adds a big capacitor to the "modulator line", and probably changes the influence so the tone "slides" back and forth, instead of jumping back and forth. C4 and R5 are already doing that to some extent.

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    \$\begingroup\$ Meta-comment: Some people will run to the backboard and start scrawling E=IR and t=RC all over it, while others look at the components and use "seat of the pants" to work out what's going on. I fall into the latter group :) \$\endgroup\$ – gbarry Oct 21 '17 at 18:08
  • \$\begingroup\$ Yes, kinda has the elements of a siren, or some kind of "danger!...danger!" sound effect. Or could emulate a squealing pig (or cow, or excited cat). But not tremendously loud, running from a nine volt source. \$\endgroup\$ – glen_geek Oct 22 '17 at 1:40

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