I have provided a basic schematic and parts list for the aquarium wave maker circuit. Here is what you will need:
*Blue plastic "double" electrical box (for household wiring) $1
*Standard electrical outlet and outlet/switch faceplate $2
*12 volt transformer and full-wave bridge (cut up an old one that you are not using. $6 for Jameco #100095)
*Power cord (cut up an old one)
*558 timer chip (Jameco #27457) $1.20
*Solid state relay Kyotto KB20C02A (Jameco #175214) $6.55
*7808 or 7809 voltage regulator (Jameco #876352) $0.56
*two 100K pots (Jameco #29103) $2.18
*two 3,300 uF capacitors (Jameco #93666) $1.22
*PN2222 transistor (Jameco #178511) $0.12
*perf board, wire, maybe a 16-pin DIP socket, misc caps and resistors $2.00
Total parts cost is about $23. Here's a link to Jameco
Notes: My circuit provided times of about 1 to 6 minutes for the on and off periods. You may want to put a 10K resistor in-line with the 100K pots. If either pot is turned too far down, the circuit will stop oscillating, so the additional fixed resistance will prevent this from happening.
This circuit does not provide the "soft start" that many commercial wavemakers tout. These motors likely use shaded poles for starting, and a soft-start controller would have to control the frequency of the AC power, not just the voltage. I find it pretty unlikely that this is what any wavemaker does, and for the price they charge, it's probably cheaper to buy a new powerhead every year! I haven't used my wavemaker long enough to know if it will kill the powerhead. I'm using an Aquaclear powerhead, and it clicks loudly upon startup, but there is no chatter. I may make another post about modifying the impeller to cope with the repeated startups.
I've experimented with using dimmers, current-limiters, etc, to control the speed of powerheads. The speed can only be reduced %10 or %20 before the motor stalls. It's not really practical without control over the frequency of the AC waveform.
The Solid-state relay in this circuit has a current limit of 2A. This mean it can control up to about 200W of powerhead.