I think I read the equivalent capacitance of a piezo buzzer is in the nF range, so without the LED is way too high pitch.

 

@Robsco
May be you will interested in this "quack-quack" oscillator...

 

I'd love to know why, or why the impedance makes such a difference, and why inverting the transistors works at all

When you swap the emitter and collector of a transistor, it still operates, but with greatly reduced gain.

Here is my possible explanation: with the transistors in their normal configuration, and the 32 Ohm speaker, one of the transistors is saturating instead of operating in the linear region, and this prevents oscillation.

Switching either transistor lowers the gain and keeps it out of saturation.

Changing to an 8 Ohm speaker also takes it out of saturation because more base current is required to saturate with the heavier load.

 

this looks a lot like other such products (Snap circuits CM-200). even the manual seem to be the same.
piezo element seem to have resonant frequency of about 4.2kHz and also functions as 20nF capacitor.

RV is likely a 50k potentiometer.

RP (photo resistor) changes from about 1k in bright light to over 100k in darkness.

Standard Resistors:
R1: 100 Ω
R2: 1 kΩ
R3: 5.1 kΩ
R4: 10 kΩ
R5: 100 kΩ

Capacitors:
C1: 0.02 µF
C2: 0.1 µF
C3: 10 µF
C4: 100 µF (sometimes 10 µF depending on the specific revision)
C5: 470 µF

 

The circuit posted by @MrChips is breadboarded and simulated. Officially working. For me makes a faint buzz but I guess my speaker is to strong (10W) for these transistors
BOM
BC558 = PNP
C3198 = NPN
R 10k, R 470Ω
C = 100nF (104)
Power source = 3.7v
Speaker = 8Ω 10W (500μH inductance)

 

i think this is intended circuit. don't know if LED is really uni or bidirectional but it clamps the amplitude. using inductor 100uH 8Ohm as small speaker and other parts also available in the kit, i get 750Hz which is in audible range. and it seem to work with both 3V and 6V.

removing D1 makes it work pulsed but frequency shoots up to 70kHz.


removing D2 makes it run even faster and amplitude is way higher.

 

Swapping the included 32 Ohm 0.5W speaker for an 8 ohm one does seem to solve all the problems.

 

Swapping the included 32 Ohm 0.5W speaker for an 8 ohm one does seem to solve all the problems.

What I figured from the schematic (if it is the on I used) is that the oscillation needs proper speaker (inductor)

 

If this was posted, I missed it: What is the circuit number for the image in post #1?

ak