The hearth study
Lynn (2014) showed participants a fire with and without its sound. Watching a fire with the crackle lowered blood pressure, and the effect grew with time; the silent fire did not have the same effect. It is one study with a modest sample, but it matches what most people report: the sound is the calming part.
What it masks
A fire recording has a broadband roar under the crackle, close to pink noise, so it covers household sound reasonably well. The crackles are irregular, which some people like and others find alerting; if you are one of the latter, run brown noise for detail work and keep the fire for reading.
Best for
Reading, reviewing, evening sessions, and long blocks where a steadier sound starts to feel clinical.
Lynn (2014), "Hearth and campfire influences on arousal and blood pressure", Evolutionary Psychology, 12(5).