An air conditioner is definitely not an energy efficient white noise generator! You are right to want to find a better source.
A table fan will produce a nice white noise using 10-25 watts depending on the model and speed setting.
My clock radio uses 5 watts when playing music. If you tuned a clock radio to a gap between stations you might find the same power consumption.
A white noise generator for sleep is not necessarily energy efficient. I looked up a few and found:
- The SleepMate 980A uses 38 Watts. Better than a room air conditioner but worse than other options above.
- The PNG (Portable Noise Generator) 200 doesn't tell you its wattage, but when relying on its batteries it can last about 2 hours on full volume, using two 9-volt alkaline batteries. Based on a mAh rating of 380 for a typical 9-volt alkaline, I figure that means the unit uses about 2.6 watts on full power.
Do you wake up if the white noise stops? If not, then one option is to use your clock radio's sleep function, set the dial between stations and set the sleep function to 59 minutes (typically the maximum setting). You should be sound asleep before the sound stops!
You're obviously interested in cutting your electricity use, you might want to check out some of my electricity saving tips, link provided below. Also, if you want to measure the energy efficiency of different devices that make a white noise, whether in your home or at the store, you can use an energy monitor like the Kill A Watt meter. Sometimes you can just borrow one from your local library, or you can buy them on the web for about $20 or so.