Sound is a compression wave, so you have areas of high pressure(peaks) and low pressure (valleys) as it propagates. What they're doing here sounds like making a standing wave that holds a low pressure zone around the fire, depriving it of oxygen.
I'm a bit rusty on my physics, but I suspect what happens is that it measures the sound when it reflects back and adjusts the frequency of the wave to put the reflection in phase with the original wave. The sum of the forward and backward components creates the standing wave.
Alternately, maybe the rapid switching between high/low pressure is enough to do it without any standing wave shenanigans. I'd guess not, but it's not my area of expertise.
I'm a bit rusty on my physics, but I suspect what happens is that it measures the sound when it reflects back and adjusts the frequency of the wave to put the reflection in phase with the original wave. The sum of the forward and backward components creates the standing wave.
http://en.wikipedia.org/wiki/Standing_wave
Alternately, maybe the rapid switching between high/low pressure is enough to do it without any standing wave shenanigans. I'd guess not, but it's not my area of expertise.