Formula for sound dissipation in air?

AI Thread Summary
The discussion addresses the equation for sound dissipation in air, highlighting that sound intensity decreases with distance due to the inverse square law, represented by I = P/(4πr²). Additionally, sound absorption is influenced by frequency and humidity, leading to attenuation that is proportional to distance. Both the inverse square law and absorption effects occur simultaneously. Understanding these principles is crucial for analyzing sound propagation in various environments. The conversation emphasizes the complexity of sound dissipation beyond simple distance calculations.
Ralphonsicus
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Is there an equation that deals with the dissipation of sound waves in air? As in, how much they die out with distance, because we know they must, otherwise you could hear me talking now!
 
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The intensity is inversely proportional to the radius squared.

That is, if a certain source has a power P and it emits pressure waves spherically, the intensity I you'll hear is

I = \frac{P}{4\pi r^2}
 
There is also some absorption, which depends on frequency (proportional to frequency squared) and humidity. This produces an attenuation which is proportional to distance (as opposed to inverse square law). Both effects occur at the same time.

See this link.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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