Dave –
Interesting idea, an acoustic pyrometer. Unfortunately:
"The speed of sound depends on temperature…"
To a point. It actually depends on density. Whilst the density of a gas is affected by its temperature, it also depends on pressure, so the confining conditions and gas flow. I think the variability of everything in a miniature boiler would be nighmarishly difficult to analyse to the depth necessary.
I don't presume to deny it would not work but could be far trickier than it seems.
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A humbling little digression…….
By comparison with Nature's been up to for some millions of years…
… bats have been using sound in the some-tens of kHz for social calls, and typically around the 100kHz mark for hunting and close-in navigation, no problem. The hunting also needs high repetition-rate chirps to aid discriminating insect prey of low sound reflectivity, from acoustically very difficult backgrounds in constant but random change. It probably uses interference patterns between the call and insect wing-beat.
Except that their upper frequency distance range is necessarily very short by signal absorption in the air and by the animal's very low call power. This is to some compensated for by high voice pressure-levels; in some species, handsomely exceeding 90 or even 100 dB re 20µPa: levels dangerous for us if within our hearing-range and at larger powers.
Think of being a little pipistrelle or horseshoe homing in on a fluttering moth against the constantly moving acoustic clutter of foliage. Just part of a very few grammes of brain working flat-out on very rapid, very complicated signal-processing necessary to control the responding flight, calls and ear-damping, while synchronising breathing with wing-flap and call. That mechanism maximises system efficiency by combining the chest muscles' contribution to exhalation with assisting the wing power-stroke. While it's at it, the brain's other departments are continuing to monitor and control the rest of the animal's physiology generally. All by instinct.
(The horseshoe bats call through their nostrils! Their characteristic facial folds are for call beam-focussing.)
Oh, and some of that compact brain must be holding some form of acoustic map memory back to the roost, especially vital to a nursing mother bat. They do have fairly good sight but that won't work in a cellar, mine or cave with no light whatsoever. Yet these lovely little creatures recall their way through what must be fiendishly complex acoustic "scenery" to where they sometimes reach.
What are we doing with ultrasonic location and ranging? (Actually, light on my car – a camera.) Using steady pulses and a string of 'beeps' to help us ease a big steel box into a shop car-park bay to the nearest foot or so usually in broad daylight, whilst knowing our "prey" is sitting perfectly still in tins and packets on the shelves….
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