Ambient Acoustic Noise equal to Maximum Solar Power Intensity

The reference sound pressure is 20 microPascal, often referred to as “limit of human hearing” in one of those super quiet rooms. Find Common sound pressures on Wikipedia “Sound pressure”. You might convert pressure to power

Pascal = Newtons/meter^2 = Newton*Meters/Meter^3 = Joules/Meter^3 = (Watts/Meter^2)/(Meters/second).

Pressure = Force/Area = Force*Distance/Area*Distance = Energy/Volume = (Power/Area)/(Velocity)

Power/Area = Pressure*Velocity = (20*10^-6 Pascal)*(340 Meters/second) in Watts/Meter^2 = 0.0068 Watts/Meter^2

But search (acoustic background noise levels) and find “Ambient background noise” about 60-70 dB and “quiet suburban neighborhoods” at 45-50 dB. “Concert hall” 25-30 dB (decibels)

Ambient Pressure Pascals = 10^(dB/10) * ReferencePressure

UrbanAmbientPressure = 10^(60/10) * 20 microPascal = 20 Pascals –> (1 atmosphere = 101325 Pascal)
UrbanAmbientPowerIntensity = PressurePascal * SpeedOfSound = 20 Pascal * 340 Meters/seconds in Watts/meter^2 = 6800 Watts/meter^2

Solar Power maximum is about 1000 Watts/Meter^2

Sound level equal to solar power:

MaximumSolarPowerIntensity is about 1000 Watts/Meter^2

AcousticPressurePascalSolar = MaximumSolarPowerIntensity/SpeedOfSound = (1000 Watts/Meter^2)/(340 Meters/second)

AcousticPressurePascalSolar = 2.94 Pascal —> Note: this is just (1000/6800) * 20 Pascal

dB for 2.94 Pascal = 10*log10(2.94 Pascal/20E-6 Pascal) = 51.67 dB based on 10 microPascal reference level

I am using Google for these calculations. They have bug in their calculator program. Log10 does not work, you have to say log10 (lower case)

So if you live near a highway, where the sound level is high, or near a beach with waves crashing you might use an acoustic harvestor rather than solar.

By the way

WindPressurePascal = (1/2) * DensityOfAir * VelocityOfAir^2

“Solar Acoustic Pressure” = 2.94 Pascal = (1/2) * (1.29 Kg/Meter^3) * (Velocity^2)

SolarAirVelocity = sqrt( (2* 2.94 Pascal)/ (1.29 Kg/Meter^3)) = 2.14 Meters/Second –> The velocity of air at density 1.29 kg/m^3 to produce a pressure equivalent to acoustic power equal to 1000 Watts/Meter^2.

This is hard to write in text. Better to make a spreadsheet of HTML/Javascript model that has all the piece connected. Then you check it, and check it, and check it, measure and tests and keep improving. “1% inspiration, 99% perspiration” – Edison

Note: The Wikipedia article on “sound pressure” lists “thermoacoustic device” with sound pressure level of 12600 Pascal. And it is hot, so the velocity is higher. PowerIntensity = 12600 Pascal * 1500 meter/second = 18.9 MegaWatts/meter^2

Richard Collins, The Internet Foundation