Earlier quoted context omitted.
Is there anyway to create an http stream of your output? I have a home automation on Hubitat to play a 10-hour brown noise file, hosted on a home Ubuntu server, created in Audition to play for night time on a Sonos speaker. Would love to get rid of the file and just get a live generated output.
Honestly your solution is probably already the simplest unless you're short for disk space. Maybe someone knows a way to make Ubuntu create a special file that contains a buffer with brown noise, like one of those old tape to CD converters, so that the system sees a music file but it just keeps going. It sounds like a lot of work. Using 'play -n synth brown' is easy if it's an option. I'd probably use a sound file if…
mkfifo brown.wav
sox -n brown.wav synth brown
?