physics_of_sound_II.ipynb

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    "# The Physics of Sound, Part II\n",
    "\n",
    "[return to main page](index.ipynb)\n",
    "\n",
    "## Preparations\n",
    "\n",
    "For this exercise we need the [Sound Field Synthesis Toolbox](http://sfstoolbox.org);"
   ]
  },
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   "source": [
    "import sfs  # tested for 0.5.0"
   ]
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   "source": [
    "And some other stuff:"
   ]
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   "source": [
    "# remove \"inline\" to get a separate plotting window:\n",
    "%matplotlib inline  \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy.core.umath_tests import inner1d"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "A grid for computation and plotting:"
   ]
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   "source": [
    "grid = sfs.util.xyz_grid([-2, 2], [-2, 2], 0, spacing=0.01)"
   ]
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   "source": [
    "## Boundary Conditions\n",
    "\n",
    "So far, we have only considered so-called free-field propagation where no boundary conditions apply. However, free-field propagation is an invalid assumption in most practical applications as walls and obstacles are present. These objects imply boundary conditions to the sound pressure and/or to the particle velocity. Hence, the complete solution of the wave equation has to obey these conditions.  \n",
    "\n",
    "<img src=\"data/volume.png\" width=\"300\"/>\n",
    "\n",
    "Lets assume the scenario above with a bounded volume $V$ and its boundary $\\partial V$ with the boundary normal $\\mathbf n$.  \n",
    "We classify three types of boundary conditions:\n",
    "\n",
    "1. Dirichlet: $P (\\mathbf x_0, \\omega) = F_D(\\mathbf  x_0, \\omega)$,\n",
    "2. Neumann: $\\frac{\\partial}{\\partial \\mathbf n} P (\\mathbf x_0, \\omega) = F_N(\\mathbf x_0, \\omega)$,\n",
    "3. Robin: $\\frac{\\partial}{\\partial \\mathbf n} P (x_0, ω) + j\\sigma(\\mathbf x_0, \\omega)P(\\mathbf x_0, \\omega) = F_R (\\mathbf x_0, \\omega)$\n",
    "\n",
    "with $\\mathbf x_0 \\in \\partial V$. As special case, the homogeneous boundary conditions are defined by\n",
    "\n",
    "1. Dirichlet: $F_D(\\mathbf  x_0, \\omega) = 0$ aka. sound soft\n",
    "2. Neumann:  $F_N(\\mathbf  x_0, \\omega) = 0$ aka. sound hard/rigid\n",
    "3. Robin:  $F_R(\\mathbf  x_0, \\omega) = 0$ aka. mixed"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: As a little repetition, what is denoted by $P(\\mathbf x, \\omega)$, again?"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
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   "cell_type": "markdown",
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   "source": [
    "*Exercise*: What does the notation $\\frac{\\partial}{\\partial \\mathbf n} P (\\mathbf x_0, \\omega)$ mean?"
   ]
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   "source": [
    " "
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   "source": [
    "## The Complete Solution of the Wave Equation\n",
    "\n",
    "In the [last exercise](physics_of_sound_I.ipynb), we got to know the inhomogeneous Helmholtz equation\n",
    "\n",
    "$$\\Delta P(\\mathbf x, \\omega) + \\left(\\frac{\\omega}{c}\\right)^2 P(\\mathbf x, \\omega) = -Q(\\mathbf x, \\omega)$$\n",
    "\n",
    "as the temporal Fourier transform of the inhomogeneous wave equation.\n",
    "\n",
    "*Exercise*: As a little repetition, what is denoted by $Q(\\mathbf x, \\omega)$, again?"
   ]
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    "<img src=\"data/general.png\" width=\"300\"/>\n",
    "\n",
    "The solution of inhomogeneous Helmholtz equation for a bounded region splits up into two parts\n",
    "\n",
    "1. Contribution by the inhomogeneity $Q(\\mathbf x, \\omega)$ inside $V$\n",
    "2. Contribution by the inhomogeneous boundary conditions imposed on $\\partial V$\n",
    "\n",
    "Before going into detail with these two contributions, we need to introduce a important tool called the Green's function.\n",
    "\n",
    "### The Green's Function\n",
    "\n",
    "We got to know solutions of the inhomogeneous Helmholtz equation for specific $Q(\\mathbf x, \\omega)$, like e.g. the plane wave, the point source, or the line source. The Green's function $G(\\mathbf x|\\mathbf x_0 , \\omega)$ is a versatile tool to express the solution of inhomogeneous Helmholtz Equation for any given density $Q(\\mathbf x, \\omega)$. It is the solution of the inhomogeneous Helmholtz Equation for a spatio(-temporal) Dirac pulse at $\\mathbf x_0$ as inhomogeneity fulfilling potential initial and boundary conditions. Its density spectrum is hence defined \n",
    "\n",
    "$$Q_{G}(\\mathbf x | \\mathbf x_0, \\omega) = \\delta(\\mathbf x - \\mathbf x_0) = \\delta(x-x_0)\\delta(y-y_0)\\delta(z-z_0)$$ \n",
    "\n",
    "for the 3D case. The Green's Function fulfills the inhomogeneous Helmholtz Equation\n",
    "\n",
    "$$\\Delta G(\\mathbf x|\\mathbf x_0 , \\omega) + \\left(\\frac{\\omega}{c}\\right)^2 G(\\mathbf x|\\mathbf x_0 , \\omega) = - \\delta(\\mathbf x - \\mathbf x_0)\\,.$$\n",
    "\n",
    "#### Reciprocity Principle\n",
    "\n",
    "In acoustics, generally the reciprocity principle holds which also includes the Green's function.\n",
    "\n",
    "*Exercise*: What does the reciprocity principle tell us?"
   ]
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    " "
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    "#### Translation Invariance\n",
    "\n",
    "Under free field propagation (no boundaries) the Green's Function $G(\\mathbf x|\\mathbf x_0 , \\omega)$ is also called the free-field Green's function $G_0(\\mathbf x|\\mathbf x_0 , \\omega)$. Here, the translation invariance $G_0(\\mathbf x|\\mathbf x_0 , \\omega) = G_0(\\mathbf x - \\mathbf x_0 , \\omega)$  holds. For three- or two-dimensional scenarios the free-field Green's function is a [point source](physics_of_sound_I-solutions.ipynb#Point-Source) or [line source](physics_of_sound_I-solutions.ipynb#Line-Source), respectively.\n",
    "\n",
    "*Exercise: What is the physical meaning of the translation invariance?*"
   ]
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    " "
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   "source": [
    "*Exercise: Why does an ordinary room, e.g. a seminar room, not fulfill the translation invariance*?"
   ]
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    "### Contribution by the inhomegenity $Q(\\mathbf x, \\omega)$ inside $V$\n",
    "\n",
    "We will now see how to use the Green's Function to express the solution of the inhomogeneous Helmholtz equation for an arbitrary  inhomogeneity $Q(\\mathbf x, \\omega)$.\n",
    "\n",
    "*Exercise: Calculate the following Integral using the properties of the Dirac impulse.*\n",
    "\n",
    "$$\\int_{V} Q(\\mathbf x_0, \\omega) \\delta(\\mathbf x - \\mathbf x_0) \n",
    "\\,\\mathrm d V(\\mathbf x_0) \\text{ with } \\mathbf x \\in V\n",
    "$$"
   ]
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    "Now we know, how the density $Q(\\mathbf x, \\omega)$ of the sound field $P(\\mathbf x, \\omega)$ and the density $\\delta(\\mathbf x - \\mathbf x_0)$ of the Green's function $G(\\mathbf x|\\mathbf x_0 , \\omega)$ are related."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise: Keeping the linearity of the Helmholtz Equation in mind, how are $P(\\mathbf x, \\omega)$ and $G(\\mathbf x|\\mathbf x_0 , \\omega)$ related? What is the physical meaning of this result?* "
   ]
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    "### Contribution by the inhomogeneous boundary conditions imposed on $\\partial V$\n",
    "\n",
    "We have now handled any inhomogeneity being present inside $V$. Hence, the contribution from the boundary states the general solution of the **homogeneous** Helmholtz equation fulfilling the inhomogeneous boundary conditions\n",
    "\n",
    "$$\n",
    "P(\\mathbf{x},\\omega) =\n",
    "\\oint_{\\partial V}\\biggl[P(\\mathbf{x}_0, \\omega)\\,\\frac{\\partial G(\\mathbf{x}-\\mathbf{x}_0, \\omega)}{\\partial \\mathbf n(\\mathbf{x}_0)}-G(\\mathbf{x}-\\mathbf{x}_0, \\omega)\n",
    "\\,\\frac{\\partial P(\\mathbf{x}_0, \\omega)}{\\partial \\mathbf n(\\mathbf{x}_0)}\\biggr]\\,\\mathrm{d}A(\\mathbf{x}_0)\n",
    "$$\n",
    "for $\\mathbf{x} \\in V$. This equation is also known as the **Kirchhoff-Helmholtz integral** or the **Helmholtz integral equation**\n",
    "\n",
    "*Exercise*: What type of sound field does $\\displaystyle \\frac{\\partial G(\\mathbf{x}-\\mathbf{x}_0, \\omega)}{\\partial \\mathbf n(\\mathbf{x}_0)}$ represent under free-field conditions in 3D?"
   ]
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   "source": [
    "Let's try out this integral for a point source positioned outside $V$"
   ]
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    "# we need some functions that are not provided by the 0.5.0 API\n",
    "\n",
    "\n",
    "def secondary_source_point_dipole(omega, c):\n",
    "    \"\"\"Create a point dipole source for use in `sfs.fd.synthesize()`.\"\"\"\n",
    "\n",
    "    def secondary_source(position, normal, grid):\n",
    "        return sfs.fd.source.point_dipole(omega, position, normal, grid, c=c)\n",
    "\n",
    "    return secondary_source\n",
    "\n",
    "\n",
    "def secondary_source_line_dipole(omega, c):\n",
    "    \"\"\"Create a line dipole source for use in `sfs.fd.synthesize()`.\"\"\"\n",
    "\n",
    "    def secondary_source(position, normal, grid):\n",
    "        return sfs.fd.source.line_dipole(omega, position, normal, grid, c=c)\n",
    "\n",
    "    return secondary_source"
   ]
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = -2, 0, 0  # position (metre)\n",
    "f = 343*2  # time-frequency (Hz)\n",
    "omega = 2 * np.pi * f  # angular frequency (rad/s)\n",
    "\n",
    "N = 2**7\n",
    "array = sfs.array.circular(N=N, R=1)\n",
    "x0 = np.array([array.x[:, 0], array.x[:, 1], array.x[:, 2]])\n",
    "\n",
    "# pressure at boundary, i.e. array coordinates\n",
    "p = sfs.fd.source.point(omega, xs, x0)\n",
    "\n",
    "# pressure gradient at boundary\n",
    "v = sfs.fd.source.point_velocity(omega, xs, x0)\n",
    "v *= -1j * sfs.default.rho0 * omega\n",
    "# split pressure gradient into components for x,y,z\n",
    "vx, vy, vz = sfs.util.as_xyz_components(v)\n",
    "# dot product of pressure gradient and boundary normal n0\n",
    "v_n0 = vx*array.n[:, 0] + vy*array.n[:, 1] + vz*array.n[:, 2]\n",
    "\n",
    "p_dipoles = sfs.fd.synthesize(p, np.ones(N),\n",
    "                              array,\n",
    "                              secondary_source_point_dipole(omega, 343),\n",
    "                              grid=grid)\n",
    "\n",
    "p_monopoles = sfs.fd.synthesize(-v_n0, np.ones(N),\n",
    "                                array,\n",
    "                                sfs.fd.secondary_source_point(omega, 343),\n",
    "                                grid=grid)\n",
    "\n",
    "sfs.plot2d.amplitude(4*np.pi*(p_dipoles + p_monopoles), grid)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: What happens, if you put the point source inside the circle?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: Can you explain the observation from above? Hind: Is the volume $V$ free of inhomogeneities?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions\n",
    "\n",
    "If you had problems solving some of the exercises, don't despair!\n",
    "Have a look at the [example solutions](physics_of_sound_II-solutions.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p xmlns:dct=\"http://purl.org/dc/terms/\">\n",
    "  <a rel=\"license\"\n",
    "     href=\"http://creativecommons.org/publicdomain/zero/1.0/\">\n",
    "    <img src=\"http://i.creativecommons.org/p/zero/1.0/88x31.png\" style=\"border-style: none;\" alt=\"CC0\" />\n",
    "  </a>\n",
    "  <br />\n",
    "  To the extent possible under law,\n",
    "  <span rel=\"dct:publisher\" resource=\"[_:publisher]\">the person who associated CC0</span>\n",
    "  with this work has waived all copyright and related or neighboring\n",
    "  rights to this work.\n",
    "</p>"
   ]
  }
 ],
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