Yelling for a Good Reason
The issue that helped instigate the issue in the previous post was How long would you have to yell to heat a cup of coffee?, which Zz had linked to.
The analysis is fine up until this point
The average human yells at about 80 decibels, which carries along with it about .001 watts of energy
The 0 dB reference for sound energy is 10-12 Watts, so 8 orders of magnitude higher is not a milliWatt. They get this right a little later on.
The average person whispers at about 40 decibels, which translates out to about 10-8 (sic) watts.
Go up by 40 dB, and you get 4 orders of magnitude in power, or 10-4 Watts. But I also read that “loud speech” is equated to 90 dB, not 80 dB, so I’m not sure where the error truly lies. If the power in Watts is what they wanted to use then their answer is fine, but if they really meant 80 dB then the answer is too small by a factor of 10.
When I first saw this problem, it was in the form of a claim that it would take 8 years of yelling, and that fits if you yell at somewhere around 83 dB. The point is that sound doesn’t carry much energy, which is one reason behind Nick’s calculation about how the Electrons per Song on an iPod has been decreasing, and how it’s possible that you can run one for 10 hours on a 3.7 V battery with only 73 mAh of capacity. That’s just 2.7 Joules, but even at 110 dB, this would only represent 1 Joule of sound energy during that span.
Pretty amazing how sensitive ears are to small amounts of energy. Also pretty scary how much energy it takes to heat water.