What about 1/(distance)² ?
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Replying to @L_G_R_R
that's only true for spherical sources! think about a sound wave .. the reason you place your hands around your mouth is to essentially to change this so that the intensity drops off more slowly
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Replying to @InertialObservr @L_G_R_R
Laser intensity drops off as 1/r² if you are far away from the focus of the beam. Gaussian beams follow a hyperbola, so far from the focus, the beam profile has a width w(r) that grows linearly with r, so the average intensity goes as 1/r².pic.twitter.com/zK51vO9Vox
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also I think that placing your hand over your mouth / using a megaphone / etc only changes the constant in front of the 1/r² scaling for sound, not the scaling itself
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Replying to @bencbartlett @L_G_R_R
right but i'm talking about the incident intensity, standing 10 yards away cupping my hands would lead to a higher incident intensity
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Replying to @InertialObservr @L_G_R_R
yeah, I guess I was confused by "so that the intensity drops off more slowly" I interpreted "drops off more slowly" to mean goes as O(1/r^k) for k<2, not just changing the constant of the intensity, but I guess that's the computer scientist in me being pedantic
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that's a fair point though .. i can see how that could be confusing
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