{"id":44643,"date":"2025-06-15T12:10:04","date_gmt":"2025-06-15T12:10:04","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=44643"},"modified":"2025-06-15T12:10:04","modified_gmt":"2025-06-15T12:10:04","slug":"constructive-interference","status":"publish","type":"post","link":"https:\/\/kingarthur.com\/songwriter\/2025\/06\/15\/constructive-interference\/","title":{"rendered":"Constructive Interference"},"content":{"rendered":"<p><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XIV\/Constructive-Interference-Best-Of.mp3\">Constructive-Interference-Best-Of.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XIV\/Constructive-Interference-Best-Of.mp4\">Constructive-Interference-Best-Of.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XIV\/Constructive-Interference.mp3\">Constructive-Interference.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XIV\/Constructive-Interference.mp4\">Constructive-Interference.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XIV\/Constructive-Interference-intro.mp3\">Constructive-Interference-intro.mp3<\/a><\/p>\n<p>[Verse 1]<br \/>\nHow a standing wave<br \/>\nDoes behave<br \/>\nDid you hear the scoop<br \/>\nOn the positive feedback loop<\/p>\n<p>[Bridge]<br \/>\n[Instrumental, Guitar Solo, Feedback Guitar, Bass]<br \/>\nPhase alignment<br \/>\n(Energy reinforcement)<\/p>\n<p>[Chorus]<br \/>\nConstructive interference<br \/>\n(Maximum motion)<br \/>\nReflection reference<br \/>\n(Resonant notion)<\/p>\n<p>[Instrumental, Saxophone Solo]<\/p>\n<p>[Verse 2]<br \/>\nResonance and dissidence<br \/>\nPhase and delay<br \/>\nResonant frequency<br \/>\nNodes and anomalies<\/p>\n<p>[Bridge]<br \/>\n[Instrumental, Guitar Solo, Feedback Guitar, Bass]<br \/>\nPhase alignment<br \/>\n(Energy reinforcement)<\/p>\n<p>[Chorus]<br \/>\nConstructive interference<br \/>\n(Maximum motion)<br \/>\nReflection reference<br \/>\n(Resonant notion)<\/p>\n<p>[Verse 3]<br \/>\nCombined attitude of amplitudes<br \/>\nSuperposition superstition<br \/>\nPickups near the amp<br \/>\nFeedback starts to ramp<\/p>\n<p>[Bridge]<br \/>\n[Instrumental, Guitar Solo, Feedback Guitar, Bass]<br \/>\nPhase alignment<br \/>\n(Energy reinforcement)<\/p>\n<p>[Chorus]<br \/>\nConstructive interference<br \/>\n(Maximum motion)<br \/>\nReflection reference<br \/>\n(Resonant notion)<\/p>\n<p>[Outro]<br \/>\n[Instrumental, Guitar Solo, Feedback Guitar, Bass]<br \/>\nPhase alignment<br \/>\n(Energy reinforcement)<\/p>\n<p>ABOUT THE SONG<\/p>\n<p data-start=\"0\" data-end=\"247\">The physics of a sound wave that reinforces itself \u2014 such as in a <strong data-start=\"66\" data-end=\"83\">standing wave<\/strong> or <strong data-start=\"87\" data-end=\"108\">acoustic feedback<\/strong> \u2014 relies on <strong data-start=\"121\" data-end=\"150\">constructive interference<\/strong>, <strong data-start=\"152\" data-end=\"165\">resonance<\/strong>, and <strong data-start=\"171\" data-end=\"198\">positive feedback loops<\/strong>. Here&#8217;s a breakdown of how these phenomena work:<\/p>\n<h3 data-start=\"254\" data-end=\"282\">1. <strong data-start=\"264\" data-end=\"282\">Standing Waves<\/strong><\/h3>\n<p data-start=\"284\" data-end=\"479\"><strong data-start=\"284\" data-end=\"302\">Standing waves<\/strong> occur when two sound waves of the same frequency and amplitude travel in opposite directions and interfere. This typically happens in enclosed spaces or along a string or pipe.<\/p>\n<p data-start=\"481\" data-end=\"502\"><strong data-start=\"481\" data-end=\"502\">Physics involved:<\/strong><\/p>\n<ul data-start=\"503\" data-end=\"966\">\n<li data-start=\"503\" data-end=\"566\">\n<p data-start=\"505\" data-end=\"566\"><strong data-start=\"505\" data-end=\"522\">Superposition<\/strong>: When two waves meet, their amplitudes add.<\/p>\n<\/li>\n<li data-start=\"567\" data-end=\"731\">\n<p data-start=\"569\" data-end=\"593\"><strong data-start=\"569\" data-end=\"592\">Nodes and antinodes<\/strong>:<\/p>\n<ul data-start=\"596\" data-end=\"731\">\n<li data-start=\"596\" data-end=\"657\">\n<p data-start=\"598\" data-end=\"657\"><strong data-start=\"598\" data-end=\"607\">Nodes<\/strong>: Points of <em data-start=\"619\" data-end=\"645\">destructive interference<\/em>, no motion.<\/p>\n<\/li>\n<li data-start=\"660\" data-end=\"731\">\n<p data-start=\"662\" data-end=\"731\"><strong data-start=\"662\" data-end=\"675\">Antinodes<\/strong>: Points of <em data-start=\"687\" data-end=\"714\">constructive interference<\/em>, maximum motion.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"732\" data-end=\"844\">\n<p data-start=\"734\" data-end=\"844\"><strong data-start=\"734\" data-end=\"757\">Boundary conditions<\/strong>: Reflections off walls (closed or open ends) determine where nodes and antinodes form.<\/p>\n<\/li>\n<li data-start=\"845\" data-end=\"963\">\n<p data-start=\"847\" data-end=\"963\"><strong data-start=\"847\" data-end=\"869\">Resonant frequency<\/strong>: Only specific frequencies (harmonics) fit perfectly into the space and reinforce themselves.<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"967\" data-end=\"1042\"><strong data-start=\"967\" data-end=\"978\">Example<\/strong>: A guitar string fixed at both ends supports standing waves at:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">fn=n(v2L)f_n = n\\left(\\frac{v}{2L}\\right)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">2<span class=\"mord mathnormal\">L<\/span><span class=\"mord mathnormal\">v<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1082\" data-end=\"1088\">Where:<\/p>\n<ul data-start=\"1089\" data-end=\"1218\">\n<li data-start=\"1089\" data-end=\"1125\">\n<p data-start=\"1091\" data-end=\"1125\"><span class=\"katex\"><span class=\"katex-mathml\">fnf_n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> = nth harmonic frequency<\/p>\n<\/li>\n<li data-start=\"1126\" data-end=\"1148\">\n<p data-start=\"1128\" data-end=\"1148\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">v<\/span><\/span><\/span><\/span> = wave speed<\/p>\n<\/li>\n<li data-start=\"1149\" data-end=\"1177\">\n<p data-start=\"1151\" data-end=\"1177\"><span class=\"katex\"><span class=\"katex-mathml\">LL<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span> = length of string<\/p>\n<\/li>\n<li data-start=\"1178\" data-end=\"1218\">\n<p data-start=\"1180\" data-end=\"1218\"><span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span> = harmonic number (1, 2, 3&#8230;)<\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"1225\" data-end=\"1278\">2. <strong data-start=\"1235\" data-end=\"1278\">Acoustic Feedback (Microphone Feedback)<\/strong><\/h3>\n<p data-start=\"1280\" data-end=\"1413\"><strong data-start=\"1280\" data-end=\"1292\">Feedback<\/strong> happens when a sound loop forms between a microphone and a speaker, causing rapid reinforcement of a specific frequency.<\/p>\n<p data-start=\"1415\" data-end=\"1436\"><strong data-start=\"1415\" data-end=\"1436\">Physics involved:<\/strong><\/p>\n<ul data-start=\"1437\" data-end=\"2003\">\n<li data-start=\"1437\" data-end=\"1613\">\n<p data-start=\"1439\" data-end=\"1466\"><strong data-start=\"1439\" data-end=\"1465\">Positive feedback loop<\/strong>:<\/p>\n<ol data-start=\"1469\" data-end=\"1613\">\n<li data-start=\"1469\" data-end=\"1513\">\n<p data-start=\"1472\" data-end=\"1513\">Microphone picks up sound from a speaker.<\/p>\n<\/li>\n<li data-start=\"1516\" data-end=\"1539\">\n<p data-start=\"1519\" data-end=\"1539\">Amplifier boosts it.<\/p>\n<\/li>\n<li data-start=\"1542\" data-end=\"1565\">\n<p data-start=\"1545\" data-end=\"1565\">Speaker re-emits it.<\/p>\n<\/li>\n<li data-start=\"1568\" data-end=\"1613\">\n<p data-start=\"1571\" data-end=\"1613\">Microphone picks it up again&#8230; and so on.<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li data-start=\"1614\" data-end=\"1759\">\n<p data-start=\"1616\" data-end=\"1759\"><strong data-start=\"1616\" data-end=\"1629\">Resonance<\/strong>: The loop amplifies only certain frequencies\u2014typically those at or near the <strong data-start=\"1706\" data-end=\"1730\">resonant frequencies<\/strong> of the room or audio system.<\/p>\n<\/li>\n<li data-start=\"1760\" data-end=\"1874\">\n<p data-start=\"1762\" data-end=\"1874\"><strong data-start=\"1762\" data-end=\"1791\">Constructive interference<\/strong>: If the sound wave&#8217;s phase aligns on each loop, the amplitude grows exponentially.<\/p>\n<\/li>\n<li data-start=\"1875\" data-end=\"2000\">\n<p data-start=\"1877\" data-end=\"2000\"><strong data-start=\"1877\" data-end=\"1896\">Phase and delay<\/strong>: A small time delay (usually milliseconds) determines whether the wave will cancel or reinforce itself.<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2004\" data-end=\"2067\"><strong data-start=\"2004\" data-end=\"2030\">Mathematical condition<\/strong> (Barkhausen criterion for feedback):<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Loop\u00a0gain\u22651andtotal\u00a0phase\u00a0shift=0\u2218\u00a0or\u00a0multiple\u00a0of\u00a0360\u2218\\text{Loop gain} \\geq 1 \\quad \\text{and} \\quad \\text{total phase shift} = 0^\\circ \\text{ or multiple of } 360^\\circ<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">Loop\u00a0gain<\/span><\/span><span class=\"mrel\">\u2265<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mord text\"><span class=\"mord\">and<\/span><\/span><span class=\"mord text\"><span class=\"mord\">total\u00a0phase\u00a0shift<\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord text\"><span class=\"mord\">\u00a0or\u00a0multiple\u00a0of\u00a0<\/span><\/span><span class=\"mord\">36<\/span><span class=\"mord\">0<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 data-start=\"2196\" data-end=\"2220\">Unifying Concepts<\/h3>\n<p data-start=\"2222\" data-end=\"2263\">Both standing waves and feedback involve:<\/p>\n<ul data-start=\"2264\" data-end=\"2394\">\n<li data-start=\"2264\" data-end=\"2301\">\n<p data-start=\"2266\" data-end=\"2301\"><strong data-start=\"2266\" data-end=\"2280\">Reflection<\/strong> and <strong data-start=\"2285\" data-end=\"2301\">interference<\/strong><\/p>\n<\/li>\n<li data-start=\"2302\" data-end=\"2323\">\n<p data-start=\"2304\" data-end=\"2323\"><strong data-start=\"2304\" data-end=\"2323\">Phase alignment<\/strong><\/p>\n<\/li>\n<li data-start=\"2324\" data-end=\"2357\">\n<p data-start=\"2326\" data-end=\"2357\"><strong data-start=\"2326\" data-end=\"2357\">Resonant frequency matching<\/strong><\/p>\n<\/li>\n<li data-start=\"2358\" data-end=\"2394\">\n<p data-start=\"2360\" data-end=\"2394\"><strong data-start=\"2360\" data-end=\"2394\">Energy reinforcement over time<\/strong><\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"2401\" data-end=\"2427\">\u00a0Real-World Examples<\/h3>\n<ul data-start=\"2429\" data-end=\"2751\">\n<li data-start=\"2429\" data-end=\"2515\">\n<p data-start=\"2431\" data-end=\"2515\"><strong data-start=\"2431\" data-end=\"2454\">Musical instruments<\/strong>: Resonating air columns (flutes, organs) use standing waves.<\/p>\n<\/li>\n<li data-start=\"2516\" data-end=\"2593\">\n<p data-start=\"2518\" data-end=\"2593\"><strong data-start=\"2518\" data-end=\"2536\">Room acoustics<\/strong>: Standing waves can cause &#8220;dead spots&#8221; or &#8220;boomy&#8221; tones.<\/p>\n<\/li>\n<li data-start=\"2594\" data-end=\"2658\">\n<p data-start=\"2596\" data-end=\"2658\"><strong data-start=\"2596\" data-end=\"2610\">PA systems<\/strong>: Improper mic placement causes feedback squeal.<\/p>\n<\/li>\n<li data-start=\"2659\" data-end=\"2751\">\n<p data-start=\"2661\" data-end=\"2751\"><strong data-start=\"2661\" data-end=\"2701\">Singular note feedback in rock music<\/strong>: Guitar pickups near amp create musical feedback.<\/p>\n<\/li>\n<\/ul>\n<h2>This song could also be applied to political protests. <a href=\"http:\/\/everything.membrane.com\/trumpenomics-the-decline-of-the-us\/\">Trumpenomics: The Decline of the US<\/a><\/h2>\n<h3>From the album &#8220;<a href=\"\/songwriter\/tag\/sound-sound\/\">Sound Sound<\/a>&#8220;<\/h3>\n<h2><a href=\"http:\/\/membrane.com\/global_warming\/\">The Human Induced Climate Change Experiment<\/a><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Constructive-Interference-Best-Of.mp3 Constructive-Interference-Best-Of.mp4 Constructive-Interference.mp3 Constructive-Interference.mp4 Constructive-Interference-intro.mp3 [Verse 1] How a standing wave Does behave Did you hear the scoop On the positive feedback loop [Bridge] [Instrumental, Guitar Solo, Feedback Guitar, Bass] Phase alignment (Energy reinforcement) [Chorus] Constructive interference (Maximum motion) Reflection reference (Resonant notion) [Instrumental, Saxophone Solo] [Verse 2] Resonance and dissidence Phase and delay Resonant [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[3,9,14],"tags":[4137],"class_list":["post-44643","post","type-post","status-publish","format-standard","hentry","category-4d-music","category-daniel","category-lyrics","tag-sound-sound"],"_links":{"self":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/44643","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=44643"}],"version-history":[{"count":5,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/44643\/revisions"}],"predecessor-version":[{"id":44671,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/44643\/revisions\/44671"}],"wp:attachment":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=44643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=44643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=44643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}