2b:null 2c:["$","title",null,{"children":"Acoustic Impedance - or Why Don't Air Horns Break Physics? | hzsteinberg | Observable"}] 31:T490,{ function restart(particles, lines, height){ let startPoint = [50,height/2]; let spread = Math.PI/6; let speed = 2; let amplitude = 1; for(let angle = -spread; angle < spread; angle += spread/25){ particles.push(new SoundParticle(startPoint, angle, speed, amplitude)); } lines.push(new DividingLine(200, 200, 100, false)); lines.push(new DividingLine(300, 100, 50, false)); lines.push(new DividingLine(370, 50, 25, false)); lines.push(new DividingLine(440, 25, 12.5, false)); lines.push(new DividingLine(510, 12, 6, false)); lines.push(new DividingLine(590, 6, 3, false)); lines.push(new DividingLine(670, 3, 1, true)); } let s = simulation.setup(width, 200); restart(s.particles, s.lines, s.height); //click to make more sound s.context.canvas.onclick = function(event){ let x = event.layerX; let y = event.layerY; let spread = Math.PI/6; for(let angle = -spread; angle < spread; angle += spread/25){ s.particles.push(new SoundParticle([x,y], angle, 2, 1)); } } while (true) { simulation.run(s) simulation.draw(s) yield s.context.canvas; } }32:Tbc4,simulation = ({ setup: function(w, h){ return { width: w, height:h, context: DOM.context2d(w, h), particles:[], lines:[], last_t: Date.now() / 1000, } }, run: function(simulationData){ let particles = simulationData.particles; let lines = simulationData.lines; let width = simulationData.width; let height = simulationData.height; let context = simulationData.context; const t = Date.now() / 1000; const dt = Math.min(t - simulationData.last_t, 1/60); //update all particles let newParticles = []; //array of particles to have on the next frame for(var i=0;i width){ continue; } if(particles[i].dead){ continue; //kill some old particles if above a max limit } newParticles.push(particles[i]); } simulationData.last_t = t; simulationData.particles = newParticles; }, 'draw': function(simulationData){ simulationData.context.clearRect(0, 0, simulationData.width, simulationData.height); for(var i=0;i this.x; let newlyPastLine = nextPos[0] > this.x; if(currentlyPastLine != newlyPastLine){ //let distUntilLineIsHit = distFromPointToLine(currentPos, [this.x, 0]); if(currentlyPastLine === false){ //moving to the right return {oldZ: this.z1, newZ: this.z2}; }else{ return {oldZ: this.z2, newZ: this.z1}; } } return null; } calcIncidenceAngle(incomingAngle){ return ((2*Math.PI) - (incomingAngle - this.angle))+this.angle } draw(ctx, height){ ctx.beginPath(); ctx.strokeStyle = "#000"; ctx.moveTo(this.x, -this.length); ctx.lineTo(this.x,this.length); ctx.stroke(); //z-labels ctx.fillStyle = "#000000"; ctx.font = "20pt verdana"; ctx.fillText(this.z1, this.x - 30 - 20, height-10); if(this.showRightmostNumber){ ctx.fillText(this.z2, this.x + 30 - 5, height-10); } } }35:[] 2f:{"id":"00d135419c979369","slug":"acoustic-impedance-or-why-dont-air-horns-break-physics","title":"Acoustic Impedance - or Why Don't Air Horns Break Physics?","thumbnail":"e9c4a7f83b012d8ca5427a3f25be9a303901dd38291d9b4cee6d591b017ed66e","access_level":"public","create_time":"$D2019-07-10T17:22:51.634Z","update_time":"$D2019-07-11T19:57:29.826Z","view_time":null,"first_public_time":"$D2019-07-29T17:22:51.627Z","has_unpublished_edits":null,"fork":false,"stars":17,"starred":false,"owner":{"type":"team","id":"dac515665f0522b2","login":"hzsteinberg","name":"","avatar_url":"https://avatars-next.observableusercontent.com/a6dcaef5abbec7806d67ff132df550fef376ba5e0176b83540b7a9222638baef","tier":"starter_2024"},"version":434,"publish_version":434,"role":null,"authored":false,"authors":[{"type":"individual","id":"f7b5deb57504c1a2","login":"hzsteinberg","name":"","avatar_url":"https://avatars-next.observableusercontent.com/a6dcaef5abbec7806d67ff132df550fef376ba5e0176b83540b7a9222638baef","tier":null}],"members":[{"type":"individual","id":"f7b5deb57504c1a2","login":"hzsteinberg","name":"","avatar_url":"https://avatars-next.observableusercontent.com/a6dcaef5abbec7806d67ff132df550fef376ba5e0176b83540b7a9222638baef","tier":null,"role":"editor"}],"comments":[{"id":"3724367c1e0386e8","reply_to_id":null,"content":"It looks like your simulation doesn't account for distance traveled past the reflection point when calculating a reflection, causing some jaggedness in the reflected front. This becomes much more apparent if you decrease the simulation step size.\n\n(sorry, \"increase\")","create_time":"$D2020-12-11T22:17:38.714Z","update_time":"$D2020-12-11T22:20:29.782Z","resolved":false,"user":{"type":"individual","id":"07362516b5994994","login":"mootari","name":"Fabian Iwand","avatar_url":"https://avatars-next.observableusercontent.com/0d7defa821f38094c03bad23b9b360a5364e6e97e21fc238c39ddc48db7994ad","tier":null}}],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Acoustic Impedance - or Why Don't Air Horns Break Physics?","cells":[{"id":0,"value":"md`# Acoustic Impedance - or Why Don't Air Horns Break Physics?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"//inspired by https://www.youtube.com/watch?v=Q1YPZ-04dag\n//and https://www.youtube.com/watch?v=vcSc16tnVqk\n//and https://radiopaedia.org/articles/acoustic-impedance has some impedance values for bodies!\n\nmd`\n\nAcoustic Impedance is a property of a material that reflects how sound reflects and travels through it.\n\nIt's ${tex `z(x) = \\rho(x) / c(x)`} where ${tex `\\rho`} is the pressure and c is the speed of sound in a material.\n\n(this model only works for certain ranges of frequences - the same material can have a different impedance for waves with different frequencies!)\n\nsay you have a sound wave with 100 J of energy, and it passes into some higher-density air. how does the impedance change?\n\nEquations: \n ${tex.block`\\text{ \\% energy reflected } = (\\frac{z_1-z_2}{z_1+z_2})^2 `}\n\n ${tex.block`\\text{ \\% energy transmitted (not reflected)} = (\\frac{4z_1z_2}{z_1+z_2})^2 `}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"{\n function restart(particles, lines, height){\n let startPoint = [50,height/2];\n let spread = Math.PI/6;\n let speed = 1;\n let amplitude = 1;\n for(let angle = -spread; angle < spread; angle += spread/25){\n particles.push(new SoundParticle(startPoint, angle, speed, amplitude)); \n }\n lines.push(new DividingLine(200, 0.5, 1));\n lines.push(new DividingLine(400, 1, 20));\n lines.push(new DividingLine(600, 20, 1));\n lines.push(new DividingLine(800, 1, 1));\n }\n \n let s = simulation.setup(width, 500);\n restart(s.particles, s.lines, s.height);\n \n //click to make more sound\n s.context.canvas.onclick = function(event){\n let x = event.layerX;\n let y = event.layerY;\n for(let angle = 0; angle < Math.PI*2; angle += Math.PI/60){\n s.particles.push(new SoundParticle([x,y], angle, 1, 1)); \n }\n }\n \n while (true) {\n simulation.run(s)\n simulation.draw(s)\n yield s.context.canvas;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":316,"value":"md`\n_Click above to make some noise!_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"md`Impedance is pressure / speed of sound. It's also the force that resists a sound wave as it travels through some object. Mountains that reflect sound have high impedance, while air (which conducts sound very well) has low impedance. It's like resistance in electrical circuits.\n\n_Click to scream angrily at a wall, and watch the sound bounce off!_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":364,"value":"{\n function restart(particles, lines, height){\n let startPoint = [50,height/2];\n let spread = Math.PI/6;\n let speed = 2;\n let amplitude = 1;\n for(let angle = -spread; angle < spread; angle += spread/25){\n particles.push(new SoundParticle(startPoint, angle, speed, amplitude)); \n }\n lines.push(new DividingLine(300, 1, 2000));\n }\n \n let s = simulation.setup(width, 200);\n restart(s.particles, s.lines, s.height);\n \n //click to make more sound\n s.context.canvas.onclick = function(event){\n let x = event.layerX;\n let y = event.layerY;\n let spread = Math.PI/6;\n for(let angle = -spread; angle < spread; angle += spread/25){\n s.particles.push(new SoundParticle([x,y], angle, 2, 1)); \n }\n }\n \n while (true) {\n simulation.run(s)\n simulation.draw(s)\n yield s.context.canvas;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":319,"value":"md`\nWhy do air horns make things sound louder? It's not using any energy, or that would violate the conservation of energy. Instead - air in an instrument has very high impedance, and air outside has a low impedance. This means that without accounting for impedance, most of the energy in a sound wave made by an instrument will just reflect off the outside of the instrument:\n\n_(Click to the left, and see how most of the pressure wave reflects off the exit of the instrument:)_\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":321,"value":"{\n function restart(particles, lines, height){\n let startPoint = [50,height/2];\n let spread = Math.PI/6;\n let speed = 2;\n let amplitude = 1;\n for(let angle = -spread; angle < spread; angle += spread/25){\n particles.push(new SoundParticle(startPoint, angle, speed, amplitude)); \n }\n lines.push(new DividingLine(670, 200, 1));\n }\n \n let s = simulation.setup(width, 200);\n restart(s.particles, s.lines, s.height);\n \n //click to make more sound\n s.context.canvas.onclick = function(event){\n let x = event.layerX;\n let y = event.layerY;\n let spread = Math.PI/6;\n for(let angle = -spread; angle < spread; angle += spread/25){\n s.particles.push(new SoundParticle([x,y], angle, 2, 1)); \n }\n }\n \n while (true) {\n simulation.run(s)\n simulation.draw(s)\n yield s.context.canvas;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":329,"value":"md`\nA horn gradually reduces the impedance in a series of steps, like a transformer, and so more of the sound wave's energy exits the horn:\n\n_Click the with-horn example below and no-horn example above at the same time, and see where the energy goes in both of them!_\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":330,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":202,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"function drawCircle(context, x,y,radius){\n context.beginPath();\n context.arc(x,y, radius, 0, 2 * Math.PI);\n context.fill();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"function vecAdd(a,b){\n return [a[0]+b[0],a[1]+b[1]];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":375,"value":"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1"}} 30:"$2f:body"