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Natural Science Forum / Physics / Acoustics / July 2007Pressure as function of distance
What is the pressure of a sound wave as a function of distance? Where does this relation come from? I think it is P(r) = 1/(4*PI*r) but I can't seem to find any references to verify this. I suppose there might be a way to derive this from kinetic gas theory, but that might be more effort than it is worth. >What is the pressure of a sound wave as a function of distance? Where >does this relation come from? I think it is [quoted text clipped - 4 lines] >might be a way to derive this from kinetic gas theory, but that might be >more effort than it is worth. In the far field (ie not close to an extended source) the pressure law is simply inverse square. d  SignaturePearce Consulting http://www.pearce.uk.com On 7/9/07 6:59 AM, in article 46923f20.286949578@news.plus.net, "Don Pearce" <nospam@nospam.com> wrote: >> What is the pressure of a sound wave as a function of distance? Where >> does this relation come from? I think it is [quoted text clipped - 9 lines] > > d Maybe you misspoke. At long distances from a source, the source looks like a point. If total power is conserved, then the integrated intensity over a surface is conserved. Intensity is proportional to the SQUARE of the pressure. Thus pressure decays as 1/r and not as 1/r^2. Bill -- Support the troops. Impeach Bush. Oh, I forgot about Cheney. >On 7/9/07 6:59 AM, in article 46923f20.286949578@news.plus.net, "Don Pearce" ><nospam@nospam.com> wrote: [quoted text clipped - 19 lines] >Bill >-- Support the troops. Impeach Bush. Oh, I forgot about Cheney. The Sound Pressure Level (SPL) falls by 6dB for each doubling of distance (assuming free field propagation). That is an inverse square law. d SignaturePearce Consulting http://www.pearce.uk.com On 7/9/07 10:39 AM, in article 46927285.798620171@news.plus.net, "Don Pearce" <nospam@nospam.com> wrote: > The Sound Pressure Level (SPL) falls by 6dB for each doubling of > distance (assuming free field propagation). That is an inverse square > law. That is true. But it represents an inverse square law on intensity, not pressure. The law on pressure is merely inverse and not inverse square. Bill -- Support the troops. Impeach Bush. Oh, I forgot about Cheney. [snip] >but I can't seem to find any references to verify this. [snip] Have you tried any books on acoustics? > [snip] > [quoted text clipped - 3 lines] > > Have you tried any books on acoustics? Yes. Not many books, but of the ones I've looked at, none give it as a function of distance. > What is the pressure of a sound wave as a function of distance? > Where does this relation come from? I think it is P(r) = 1/(4*PI*r) > but I can't seem to find any references to verify this. I suppose > there might be a way to derive this from kinetic gas theory, but > that might be more effort than it is worth. Hi Chris, This website will help you. You ask for the sound pressure, our ears and the microphones are sensitive to. http://www.sengpielaudio.com/calculator-distance.htm There we have the 1/r law. Do not mix this with sound intensity or sound power. Cheers Jens >> What is the pressure of a sound wave as a function of distance? >> Where does this relation come from? I think it is P(r) = 1/(4*PI*r) [quoted text clipped - 8 lines] > There we have the 1/r law. > Do not mix this with sound intensity or sound power. This math lesson tells it all: http://www.mathdaily.com/lessons/Inverse-square_law 1/r² is the inverse-sqare law, but the sound pressure behaves like 1/r. That is the function of distance for the sensivity of microphones and our ears. Kind Regards Eberhard Sengpiel >>What is the pressure of a sound wave as a function of distance? >>Where does this relation come from? I think it is P(r) = 1/(4*PI*r) [quoted text clipped - 15 lines] > > Jens Thanks, but this does not tell me if I should use P = 1/(4*pi*r) or P = 1/r Both are consistent with the pressure relation P (is proportional to) 1/r > Jens Rodrigo wrote: >> [quoted text clipped - 3 lines] >>>there might be a way to derive this from kinetic gas theory, but >>>that might be more effort than it is worth. >> This website will help you. >> You ask for the sound pressure, our ears and the [quoted text clipped - 9 lines] > Both are consistent with the pressure relation > P (is proportional to) 1/r Hi Chris, > P = 1/(4*pi*r) This is not right. Sound intensity I is not sound pressure p Sound Intensity I = P / 4 * pi * r² Upper case P means power. 4 * pi * r² means volume of a circle (ball). Sound pressure p (lower case p) is no energy or power. "linear" sound field p proportional to 1/r p1/p2 = r2/r1 p1 = p2 times r2 / r1 "squared" energy field I proportional to 1/ r² I1/I2 = r2² /r1² I1 = I2 times r2² / r1² http://en.wikipedia.org/wiki/Sound_pressure http://en.wikipedia.org/wiki/Sound_intensity Regards Jens |
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