# Q & A: heating via sound

Q:
How much energy could be put in a sound wave?...Shockwave I'm presuming at very high decibels. I know it would be impractical, but could you heat a cup of coffee with sound?
- Devon (age 24)
Lansing
A:
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/m2. 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 105 W/m2 propagating normally. Say your cup had a depth of about 0.1m. You could have sound input to it of 106 W/m3, or 106 J/m3s. That's about 0.25 cal/cm3s, 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 104 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 103 J/m3. Propagating at 300m/s would give a flux of 3x105 W/m2, so maybe the flux could be upped a bit compared to that first calculation.

Mike W.

(published on 07/26/2011)