The equipment takes advantage of both the consistency and relative difference between the speed of sound and the speed of light to create a visual recording of the sound impulses which would arrive at the microphones after the flash of the guns being fired. An operator would wait for the flash of an enemy gun to start the film rolling and the equipment would record the signals as they arrived progressively based on their proximity to the impulse source.
The film took around five minutes to develop after which trained analysts could decode the patterns on the film and use them to work out the positions of enemy guns using a process called multilateration.
By the end of WW1 sound ranging techniques could locate enemy guns within 25m to 50m under normal atmospheric conditions and even determine the caliber, number of guns and the target. The document above gives us a great insight into how intense and chaotic the barrage of gunfire must have been to those fighting.
And just the sound link: