It is easy to make a 555 timer chip make noise.
We set up the circuit to generate square waves (equal time in the on and off states), and select our resistor and capacitor so that the oscillations are in the range of human hearing.
Then we put a speaker on the output.
If the resistor is a rheostat (or a potentiometer with one of the outside wires unused), then we can vary the pitch of the sound. The circuit looks like this in schematic form:
The circuit looks like this when built on a solderless breadboard:
Here is a close-up of the circuit:
If your project needs to make little blips or beeps when buttons are pushed, then this little circuit will do the trick. You can replace the potentiometer with a row of resistors, each with its own switch, and build a toy piano. The noises are reminiscent of early video games, which also used square waves sent to a speaker.