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@@ -48,6 +48,47 @@
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color: #0080ff;
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}
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+ .math {
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+
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+ text-align: center;
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+
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+ }
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+
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+ .math-frac {
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+
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+ display: inline-block;
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+ vertical-align: middle;
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+
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+ }
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+
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+ .math-num {
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+
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+ display: block;
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+
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+ }
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+
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+ .math-denom {
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+
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+ display: block;
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+ border-top: 1px solid;
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+
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+ }
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+
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+ .math-sqrt {
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+
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+ display: inline-block;
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+ transform: scale(1, 1.3);
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+
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+ }
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+
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+ .math-sqrt-stem {
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+
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+ display: inline-block;
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+ border-top: 1px solid;
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+ margin-top: 5px;
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+
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+ }
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+
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</style>
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</head>
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<body>
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@@ -57,11 +98,9 @@
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<div id="info"><a href="http://threejs.org" target="_blank">three.js</a> - multiple elements with text - webgl</div>
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<script src="../build/three.min.js"></script>
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- <script src="../examples/js/controls/OrbitControls.js"></script>
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+ <script src="js/controls/OrbitControls.js"></script>
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<script src="js/Detector.js"></script>
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-
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- <script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML"></script>
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<script>
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@@ -234,13 +273,52 @@
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<p>Sound waves whose geometry is determined by a single dimension, plane waves, obey the wave equation</p>
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- \[ \frac{ \partial^2 u }{ \partial r^2 } - \frac{ 1 }{ c^2 } \frac{ \partial^2 u }{ \partial t^2 } = 0 \]
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+ <!-- css math formatting inspired by http://mathquill.com/mathquill/mathquill.css -->
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+
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+ <div class="math">
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<sup>2</sup><i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>r</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ −
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ 1<sup></sup> <!-- sup for vertical alignment -->
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+ </span>
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+ <span class="math-denom">
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+ <i>c</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<sup>2</sup><i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>t</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ = 0
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+
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+ </div>
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<p>where <i>c</i> designates the speed of sound in the medium. The monochromatic solution for plane waves will be taken to be</p>
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- \[ u(r,t) = \sin( k r \pm ω t ) \]
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+ <div class="math">
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+
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+ <i>u</i>(<i>r</i>,<i>t</i>) = sin(<i>k</i><i>r</i> ± ω<i>t</i>)
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+
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+ </div>
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- <p>where ω is the frequency and \( k = ω / c \) is the wave number. The sign chosen in the argument determines the direction of movement of the waves.</p>
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+ <p>where ω is the frequency and <i>k</i>=ω/<i>c</i> is the wave number. The sign chosen in the argument determines the direction of movement of the waves.</p>
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<p>Here is a plane wave moving on a three-dimensional lattice of atoms:</p>
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@@ -284,11 +362,83 @@
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<p>Sound waves whose geometry is determined by two dimensions, cylindrical waves, obey the wave equation</p>
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- \[ \frac{ \partial^2 u }{ \partial r^2 } + \frac{ 1 }{ r } \frac{ \partial u }{ \partial r } - \frac{ 1 }{ c^2 } \frac{ \partial^2 u }{ \partial t^2 } = 0 \]
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+ <div class="math">
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<sup>2</sup><i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>r</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ +
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ 1
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+ </span>
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+ <span class="math-denom">
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+ <i>r</i>
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+ </span>
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+ </span>
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>r</i>
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+ </span>
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+ </span>
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+
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+ −
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ 1<sup></sup> <!-- sup for vertical alignment -->
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+ </span>
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+ <span class="math-denom">
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+ <i>c</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<sup>2</sup><i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>t</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ = 0
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+
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+ </div>
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<p>The monochromatic solution for cylindrical sound waves will be taken to be</p>
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- \[ u(r,t) = \frac{ \sin( k r \pm ω t ) }{ \sqrt{ r } } \]
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+ <div class="math">
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+
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+ <i>u</i>(<i>r</i>,<i>t</i>) =
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ sin(<i>k</i><i>r</i> ± ω<i>t</i>)
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+ </span>
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+ <span class="math-denom">
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+ <span class="math-sqrt">√</span><span class="math-sqrt-stem"><i>r</i>
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+ </span>
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+ </span>
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+
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+ </div>
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+
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+ <div class="math">
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+
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+</span>
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+
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+ </div>
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<p>Here is a cylindrical wave moving on a three-dimensional lattice of atoms:</p>
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@@ -354,11 +504,77 @@
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<p>Sound waves whose geometry is determined by three dimensions, spherical waves, obey the wave equation</p>
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- \[ \frac{ \partial^2 u }{ \partial r^2 } + \frac{ 2 }{ r } \frac{ \partial u }{ \partial r } - \frac{ 1 }{ c^2 } \frac{ \partial^2 u }{ \partial t^2 } = 0 \]
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+ <div class="math">
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<sup>2</sup><i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>r</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ +
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ 2
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+ </span>
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+ <span class="math-denom">
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+ <i>r</i>
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+ </span>
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+ </span>
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>r</i>
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+ </span>
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+ </span>
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+
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+ −
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ 1<sup></sup> <!-- sup for vertical alignment -->
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+ </span>
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+ <span class="math-denom">
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+ <i>c</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ ∂<sup>2</sup><i>u</i>
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+ </span>
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+ <span class="math-denom">
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+ ∂<i>t</i><sup>2</sup>
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+ </span>
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+ </span>
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+
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+ = 0
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+
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+ </div>
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<p>The monochromatic solution for spherical sound waves will be taken to be</p>
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- \[ u(r,t) = \frac{ \sin( k r \pm ω t ) }{ r } \]
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+ <div class="math">
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+
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+ <i>u</i>(<i>r</i>,<i>t</i>) =
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+
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+ <span class="math-frac">
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+ <span class="math-num">
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+ sin(<i>k</i><i>r</i> ± ω<i>t</i>)
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+ </span>
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+ <span class="math-denom">
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+ <i>r</i>
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+ </span>
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+ </span>
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+
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+ </div>
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<p>Here is a spherical wave moving on a three-dimensional lattice of atoms:</p>
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paulmasson