This idea doesn't sound practical for home use, but it does sound like something that could be done in a lab setting. Maybe it has, but I can't find a reference. Here's my thoughts.
I looked around for the sound intensity of various sources, and found that a rocket engine at 50 m gave around 100 W/m
2. Presumably that could be extrapolated to some 30 times closer, given the size of rocket engines, so I guess you can have sound intensities of up to around 10
5 W/m
2 propagating normally. Say your cup had a depth of about 0.1m. You could have sound input to it of 10
6 W/m
3, or 10
6 J/m
3s. That's about 0.25 cal/cm
3s, enough to heat the water 0.25 °C/s. You could get the coffee to around 75°C in ~200s. I'm assuming that you put some nice sound-absorbing foam on the top surface, so the sound won't mostly just reflect.
I've read of shockwaves with something like 10
4 Pa pressure excess, approaching 10% of atmospheric pressure. Since the propagating energy density goes about as the square of the pressure change, I guess this would have something like 1% of the thermal energy density of the air, or roughly 10
3 J/m
3. Propagating at 300m/s would give a flux of 3x10
5 W/m
2, so maybe the flux could be upped a bit compared to that first calculation.
Mike W.
(published on 07/26/2011)
