Getting Incoherent

But that’s just two “pure” waves – what happens when EMR is the sum of many waves of different frequencies? Try adding more and more waves of different frequencies, uniformly distributed in a small range (or band):

Code

viewof form_m2_1 = Inputs.form(
    [
        Inputs.range([1, 10], {label: "# of Waves", step: 1, value: 1}),
        Inputs.range([1, 20], {label: "Speed", step: 1, value: 10})
    ],
    {
        template: (inputs) => htl.html`<div style="display: flex; gap: 1em">
        ${inputs}
        </div>`
    }
)
NumWaves_m2 = form_m2_1[0];
speed_m2    = form_m2_1[1];

amplitude_m2 = 6;
distance_m2 = 400;
NumPoints_m2 = 1000;
wavelengths_m2 = [30,29,25,33,36,24,28,35,40,22,37];
phases_m2 = [0,0,1,0.5,2,3.1,4,4.9,1.3,.8,6];

Code

waveSum_m2 = {
    var data = [];
    for (var i = 1; i <= NumPoints_m2; i++) {
        var y = 0
        for (var k = 1; k <= NumWaves_m2; k++) {
            var j = i * distance_m2 / NumPoints_m2;
            y += amplitude_m2 * Math.sin(j * 2*Math.PI / wavelengths_m2[k] + time_m2 + phases_m2[k])
        }
        data.push([j,y]);
    }
    return data;
}

Code

waves_m2 = {
    var waves = []
    for (var i = 1; i <= wavelengths_m2.length; i++) {
        var data = [];
        for (var k = 1; k <= NumPoints_m2; k++) {
            var j = k * distance_m2 / NumPoints_m2;
            data.push([j , amplitude_m2* Math.sin(j * 2*Math.PI / wavelengths_m2[i] + time_m2 + phases_m2[i]) + amplitude_m2*2.4*(i+2)]);
        }
        waves.push(data)
    }
    return waves;
}

Code

time_m2 = {
  let i = 0;
  while (true) {
    i += speed_m2 * 0.01;
    yield i
  }
}

Code

colors_m2 = {
    var colors = []
    for (var i = 0; i < wavelengths_m2.length; i++){
        if (i < NumWaves_m2){colors.push("red")}
        else {colors.push("white")}
    }
    return colors
}

summed_wave_m2 = d3.line()(waveSum_m2);
w_m2 = d3.line()(waves_m2[0]);
svg`<svg viewBox="0 -50 400 250">
  <path d="${summed_wave_m2}" stroke="black" fill="none" />
  <path d="${d3.line()(waves_m2[0])}" stroke=${colors_m2[0]} fill="none" />
  <path d="${d3.line()(waves_m2[1])}" stroke=${colors_m2[1]} fill="none" />
  <path d="${d3.line()(waves_m2[2])}" stroke=${colors_m2[2]} fill="none" />
  <path d="${d3.line()(waves_m2[3])}" stroke=${colors_m2[3]} fill="none" />
  <path d="${d3.line()(waves_m2[4])}" stroke=${colors_m2[4]} fill="none" />
  <path d="${d3.line()(waves_m2[5])}" stroke=${colors_m2[5]} fill="none" />
  <path d="${d3.line()(waves_m2[6])}" stroke=${colors_m2[6]} fill="none" />
  <path d="${d3.line()(waves_m2[7])}" stroke=${colors_m2[7]} fill="none" />
  <path d="${d3.line()(waves_m2[8])}" stroke=${colors_m2[8]} fill="none" />
  <path d="${d3.line()(waves_m2[9])}" stroke=${colors_m2[9]} fill="none" />
  <path d="${d3.line()(waves_m2[10])}" stroke=${colors_m2[10]} fill="none" />
</svg>`