[{"data":1,"prerenderedAt":568},["ShallowReactive",2],{"site-footer-common":3,"glossary:inverse-square-law":45,"glossary-related:inverse-square-law":226},{"id":4,"extension":5,"footer":6,"meta":40,"navbar":41,"stem":43,"__hash__":44},"common\u002Fcommon.yml","yml",{"tagline":7,"links":8,"sections":9},"Acoustic cleaning intelligence for industrial fouling, soot, ash, dust and build-up.",[],[10,19,31],{"title":11,"links":12},"Product",[13,16],{"label":14,"to":15},"How it works","\u002F#product",{"label":17,"to":18},"Cost assessment","\u002F#hero",{"title":20,"links":21},"Company",[22,25,28],{"label":23,"to":24},"What we build","\u002F#about",{"label":26,"to":27},"Careers","\u002F#careers",{"label":29,"to":30},"Contact","\u002F#contact",{"title":32,"links":33},"Resources",[34,37],{"label":35,"to":36},"Blog","\u002Fresources\u002Fblog",{"label":38,"to":39},"Glossary","\u002Fglossary",{},{"links":42},[],"common","YocmZRy1AYfBbpgGVms-zhdiABlF8VTxHx6h4rDmZBA",{"id":46,"title":47,"aliases":48,"body":51,"category":207,"description":208,"extension":209,"meta":210,"navigation":211,"path":212,"relatedTerms":213,"seo":217,"sources":220,"stem":224,"term":47,"__hash__":225},"glossary\u002Fglossary\u002Finverse-square-law.md","Inverse-square law",[49,50],"1\u002Fr² law (acoustic)","geometric spreading",{"type":52,"value":53,"toc":199},"minimark",[54,74,79,82,142,146,159,163,176,180],[55,56,57,58,62,63,68,69,73],"p",{},"The ",[59,60,61],"strong",{},"inverse-square law"," states that the intensity of a point-source sound wave falls as 1\u002Fr² with distance. Expressed in ",[64,65,67],"a",{"href":66},"\u002Fglossary\u002Fdecibel","decibels",", ",[64,70,72],{"href":71},"\u002Fglossary\u002Fsound-pressure-level","SPL"," decreases by approximately 6 dB for every doubling of distance from the source in a free field.",[75,76,78],"h2",{"id":77},"worked-example-for-a-sonic-horn","Worked example for a sonic horn",[55,80,81],{},"A horn rated at 150 dB SPL at 1 m on the bell axis will produce, in free-field conditions:",[83,84,85,98],"table",{},[86,87,88],"thead",{},[89,90,91,95],"tr",{},[92,93,94],"th",{},"Distance",[92,96,97],{},"Approximate SPL",[99,100,101,110,118,126,134],"tbody",{},[89,102,103,107],{},[104,105,106],"td",{},"1 m",[104,108,109],{},"150 dB",[89,111,112,115],{},[104,113,114],{},"2 m",[104,116,117],{},"144 dB",[89,119,120,123],{},[104,121,122],{},"4 m",[104,124,125],{},"138 dB",[89,127,128,131],{},[104,129,130],{},"8 m",[104,132,133],{},"132 dB",[89,135,136,139],{},[104,137,138],{},"16 m",[104,140,141],{},"126 dB",[75,143,145],{"id":144},"where-the-rule-breaks-down","Where the rule breaks down",[55,147,148,149,153,154,158],{},"Three real conditions modify the textbook result. Inside a vessel, reflections from walls and tube banks reinforce the sound field and slow the fall-off; geometry no longer behaves as a free field. In the ",[64,150,152],{"href":151},"\u002Fglossary\u002Fnear-field-far-field","near field"," of the bell, the simple 1\u002Fr² rule does not apply. And at long distances and high frequencies, ",[64,155,157],{"href":156},"\u002Fglossary\u002Fattenuation-acoustic","attenuation"," absorbs additional energy beyond geometric spreading.",[75,160,162],{"id":161},"why-it-matters-for-noise-exposure","Why it matters for noise exposure",[55,164,165,166,170,171,175],{},"Worker exposure assessments work backwards from the inverse-square law: knowing the nameplate SPL and the operator-station distance, the predicted exposure can be compared with ",[64,167,169],{"href":168},"\u002Fglossary\u002Fosha-29-cfr-1910-95","OSHA 29 CFR 1910.95"," or ",[64,172,174],{"href":173},"\u002Fglossary\u002Feu-directive-2003-10-ec","EU Directive 2003\u002F10\u002FEC"," action levels.",[75,177,179],{"id":178},"related-terms","Related terms",[181,182,183,189,194],"ul",{},[184,185,186],"li",{},[64,187,188],{"href":71},"Sound pressure level",[184,190,191],{},[64,192,193],{"href":156},"Attenuation (acoustic)",[184,195,196],{},[64,197,198],{"href":151},"Near field \u002F far field",{"title":200,"searchDepth":201,"depth":201,"links":202},"",2,[203,204,205,206],{"id":77,"depth":201,"text":78},{"id":144,"depth":201,"text":145},{"id":161,"depth":201,"text":162},{"id":178,"depth":201,"text":179},"acoustics-physics","The inverse-square law states that the intensity of a point-source sound wave falls as 1\u002Fr² with distance. Expressed in decibels, SPL decreases by approximately 6 dB for every doubling of distance from the source in a free field.","md",{},true,"\u002Fglossary\u002Finverse-square-law",[214,215,216],"sound-pressure-level","attenuation-acoustic","near-field-far-field",{"title":218,"description":219},"Inverse-square law — sound pressure halves every doubling of distance","In free-field conditions sound intensity falls as 1\u002Fr². Sound pressure level drops by approximately 6 dB for each doubling of distance from the source.",[221],{"title":222,"url":223},"Wikipedia — Inverse-square law","https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FInverse-square_law","glossary\u002Finverse-square-law","EYJdDFIbE5CXCp0ONbKYLs6jeZE8zRgWkX6myn6g82k",[227,407,490],{"id":228,"title":229,"aliases":230,"body":232,"category":207,"description":388,"extension":209,"meta":389,"navigation":211,"path":71,"relatedTerms":390,"seo":395,"sources":398,"stem":405,"term":188,"__hash__":406},"glossary\u002Fglossary\u002Fsound-pressure-level.md","Sound pressure level (SPL)",[72,231],"sound pressure level dB",{"type":52,"value":233,"toc":382},[234,251,255,325,329,342,346,358,360],[55,235,236,238,239,241,242,170,246,250],{},[59,237,229],{}," is the logarithmic measure of sound pressure relative to the 20 µPa human-hearing reference, expressed in ",[64,240,67],{"href":66},". It is the primary specification figure for any ",[64,243,245],{"href":244},"\u002Fglossary\u002Fsonic-horn","sonic horn",[64,247,249],{"href":248},"\u002Fglossary\u002Facoustic-cleaner","acoustic cleaner"," and the metric used to size noise-exposure controls at the work area.",[75,252,254],{"id":253},"industrial-reference-values","Industrial reference values",[83,256,257,267],{},[86,258,259],{},[89,260,261,264],{},[92,262,263],{},"SPL (dB)",[92,265,266],{},"Reference",[99,268,269,277,285,293,301,309,317],{},[89,270,271,274],{},[104,272,273],{},"0",[104,275,276],{},"Threshold of human hearing",[89,278,279,282],{},[104,280,281],{},"60",[104,283,284],{},"Normal conversation",[89,286,287,290],{},[104,288,289],{},"120",[104,291,292],{},"Threshold of pain",[89,294,295,298],{},[104,296,297],{},"140",[104,299,300],{},"Industrial sonic horn (lower-output models)",[89,302,303,306],{},[104,304,305],{},"160",[104,307,308],{},"Typical cement \u002F ESP sonic horn",[89,310,311,314],{},[104,312,313],{},"180",[104,315,316],{},"Upper limit of pneumatic industrial sonic horns",[89,318,319,322],{},[104,320,321],{},"194",[104,323,324],{},"Theoretical maximum for an undistorted sine wave in air",[75,326,328],{"id":327},"spl-and-cleaning-effectiveness","SPL and cleaning effectiveness",[55,330,331,332,336,337,341],{},"Cleaning energy scales with intensity, which doubles for every 3 dB rise. A 150 dB horn delivers roughly twice the energy of a 147 dB horn at the same distance. SPL is not, however, the only selection criterion: ",[64,333,335],{"href":334},"\u002Fglossary\u002Ffrequency","frequency"," determines ",[64,338,340],{"href":339},"\u002Fglossary\u002Fwavelength","wavelength"," and therefore penetration. A 150 dB low-frequency horn typically out-cleans a 160 dB high-frequency horn in a large open vessel.",[75,343,345],{"id":344},"spl-and-exposure","SPL and exposure",[55,347,348,349,351,352,354,355,357],{},"Reported nameplate SPL is measured at 1 m on the bell axis. Real exposure at the work area falls with distance per the ",[64,350,61],{"href":212}," and through enclosure attenuation. Compliance with ",[64,353,169],{"href":168}," and ",[64,356,174],{"href":173}," is calculated from exposure, not from nameplate SPL.",[75,359,179],{"id":178},[181,361,362,367,372,378],{},[184,363,364],{},[64,365,366],{"href":66},"Decibel",[184,368,369],{},[64,370,371],{"href":334},"Frequency",[184,373,374],{},[64,375,377],{"href":376},"\u002Fglossary\u002Fsound-power-vs-sound-pressure","Sound power vs sound pressure",[184,379,380],{},[64,381,47],{"href":212},{"title":200,"searchDepth":201,"depth":201,"links":383},[384,385,386,387],{"id":253,"depth":201,"text":254},{"id":327,"depth":201,"text":328},{"id":344,"depth":201,"text":345},{"id":178,"depth":201,"text":179},"Sound pressure level (SPL) is the logarithmic measure of sound pressure relative to the 20 µPa human-hearing reference, expressed in decibels. It is the primary specification figure for any sonic horn or acoustic cleaner and the metric used to size noise-exposure controls at the work area.",{},[391,335,392,393,394],"decibel","sound-power-vs-sound-pressure","inverse-square-law","sonic-horn",{"title":396,"description":397},"Sound pressure level (SPL) — definition, industrial-cleaning ranges","SPL is the logarithmic measure of sound pressure in decibels relative to a 20 µPa reference. Industrial sonic horns operate at 140–180 dB SPL.",[399,402],{"title":400,"url":401},"Wikipedia — Sound pressure","https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSound_pressure",{"title":403,"url":404},"Acoustical Society of America — Sound Pressure Level","https:\u002F\u002Fasastandards.org\u002F","glossary\u002Fsound-pressure-level","ayEoQNuJweSv9WGpwDPcx5CMESsbiPd4QPUpIoyQA6M",{"id":408,"title":193,"aliases":409,"body":412,"category":207,"description":477,"extension":209,"meta":478,"navigation":211,"path":156,"relatedTerms":479,"seo":481,"sources":484,"stem":488,"term":193,"__hash__":489},"glossary\u002Fglossary\u002Fattenuation-acoustic.md",[410,411],"acoustic attenuation","sound attenuation",{"type":52,"value":413,"toc":472},[414,431,435,438,442,450,452],[55,415,416,419,420,422,423,425,426,430],{},[59,417,418],{},"Attenuation"," is the loss of acoustic energy as a sound wave propagates through a medium. It combines geometric spreading (the ",[64,421,61],{"href":212},") with absorption losses to viscosity, heat conduction and molecular relaxation. Attenuation rises sharply with ",[64,424,335],{"href":334},", which is the physical reason ",[64,427,429],{"href":428},"\u002Fglossary\u002Flow-frequency-acoustic-cleaner","low-frequency acoustic cleaners"," reach further into large industrial vessels than their high-frequency counterparts.",[75,432,434],{"id":433},"implications-for-cleaning-reach","Implications for cleaning reach",[55,436,437],{},"A 60 Hz wave loses very little energy per metre of air travel; a 400 Hz wave loses substantially more. In hot flue gas the absolute losses change but the frequency dependence remains the same. The result is that a 60 Hz horn can clean fly-ash deposits 8–10 metres from the bell, while a 400 Hz horn is generally effective only within 3–4 metres at the same nameplate SPL.",[75,439,441],{"id":440},"implications-for-noise-control","Implications for noise control",[55,443,444,445,449],{},"The same physics that lets a low-frequency horn reach deep into a vessel also lets it travel further outside the vessel. Operator-station noise control is therefore harder for low-frequency installations, and ",[64,446,448],{"href":447},"\u002Fglossary\u002Fsound-attenuation-enclosure-sonic-horn","sound-attenuation enclosures"," are sometimes added at the bell.",[75,451,179],{"id":178},[181,453,454,459,463,467],{},[184,455,456],{},[64,457,458],{"href":339},"Wavelength",[184,460,461],{},[64,462,371],{"href":334},[184,464,465],{},[64,466,47],{"href":212},[184,468,469],{},[64,470,471],{"href":447},"Sound-attenuation enclosure (sonic horn)",{"title":200,"searchDepth":201,"depth":201,"links":473},[474,475,476],{"id":433,"depth":201,"text":434},{"id":440,"depth":201,"text":441},{"id":178,"depth":201,"text":179},"Attenuation is the loss of acoustic energy as a sound wave propagates through a medium. It combines geometric spreading (the inverse-square law) with absorption losses to viscosity, heat conduction and molecular relaxation. Attenuation rises sharply with frequency, which is the physical reason low-frequency acoustic cleaners reach further into large industrial vessels than their high-frequency counterparts.",{},[340,335,393,480],"sound-attenuation-enclosure-sonic-horn",{"title":482,"description":483},"Acoustic attenuation — why low-frequency sound travels further","Attenuation is the loss of acoustic energy as a sound wave propagates. Higher frequencies attenuate faster, which is why low-frequency sonic horns reach further in industrial vessels.",[485],{"title":486,"url":487},"Wikipedia — Acoustic attenuation","https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAcoustic_attenuation","glossary\u002Fattenuation-acoustic","WuKkiYEJRYbK7QdnPPy-tGtriMZpacuaLkpTV2w-RwM",{"id":491,"title":198,"aliases":492,"body":495,"category":207,"description":555,"extension":209,"meta":556,"navigation":211,"path":151,"relatedTerms":557,"seo":558,"sources":561,"stem":565,"term":566,"__hash__":567},"glossary\u002Fglossary\u002Fnear-field-far-field.md",[493,494],"acoustic near field","acoustic far field",{"type":52,"value":496,"toc":550},[497,512,516,524,527,531,534,536],[55,498,57,499,501,502,504,505,508,509,511],{},[59,500,152],{}," is the acoustic zone immediately surrounding a sound source — typically within one ",[64,503,340],{"href":339}," — where pressure and particle velocity are out of phase and SPL does not follow a clean 1\u002Fr² fall-off. The ",[59,506,507],{},"far field"," is the region beyond, where the wave behaves as a simple radial expansion and the ",[64,510,61],{"href":212}," applies.",[75,513,515],{"id":514},"why-the-distinction-matters-for-cleaning","Why the distinction matters for cleaning",[55,517,518,519,523],{},"Cleaning targets immediately adjacent to a horn's ",[64,520,522],{"href":521},"\u002Fglossary\u002Fbell-horn","bell"," are in the near field. The pressure environment there is intense and irregular and is what actually does the cleaning. Further targets sit in the far field, where the simpler radial model predicts the SPL.",[55,525,526],{},"For a 60 Hz horn (λ ≈ 5.7 m) the near field extends several metres. For a 400 Hz horn (λ ≈ 0.85 m) the near field is much smaller. Multi-horn arrays in large vessels deliberately overlap near-field zones so every target surface sees high-intensity coverage.",[75,528,530],{"id":529},"why-it-matters-for-measurement","Why it matters for measurement",[55,532,533],{},"Nameplate SPL is normally measured at 1 m — close enough to the source that the result depends on whether that point falls in the near or far field for the horn's frequency. Apples-to-apples comparisons between vendors require knowing where the measurement was taken.",[75,535,179],{"id":178},[181,537,538,542,546],{},[184,539,540],{},[64,541,458],{"href":339},[184,543,544],{},[64,545,188],{"href":71},[184,547,548],{},[64,549,47],{"href":212},{"title":200,"searchDepth":201,"depth":201,"links":551},[552,553,554],{"id":514,"depth":201,"text":515},{"id":529,"depth":201,"text":530},{"id":178,"depth":201,"text":179},"The near field is the acoustic zone immediately surrounding a sound source — typically within one wavelength — where pressure and particle velocity are out of phase and SPL does not follow a clean 1\u002Fr² fall-off. The far field is the region beyond, where the wave behaves as a simple radial expansion and the inverse-square law applies.",{},[340,214,393],{"title":559,"description":560},"Near field and far field — measurement zones around a sonic horn","The near field is the complex acoustic zone within roughly one wavelength of the source. The far field is the simpler region beyond, where the inverse-square law applies.",[562],{"title":563,"url":564},"Wikipedia — Near and far field","https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FNear_and_far_field","glossary\u002Fnear-field-far-field","Near field and far field","gt3fuBeZGRr0VEtbkOdAg0ZuR-1fYKLBGU5D4XkzYjI",1782613716034]