For the price of a white noise machine you can buy a 10A squirrel cage blower, some mdf to make a box out of, a contactor, and a smart plug and have a white noise machine that filters your air, turns on and off from your phone, and also makes white noise. It can also act as a table to put your phone on and a charge point.
I had the two problems of poor sleep without white noise and a dog allergy and now I have neither.