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@alexalemi
Created July 23, 2014 06:37
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ipython notebook of simulated sound in racquetball court
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"worksheets": [
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simulating the Acoustics of a Racquetball Court"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook aims to simulate the auditory environment of a racquetball court in order to answer [this stackexchange question](http://physics.stackexchange.com/questions/127282/physics-of-boing-sound-in-raquetball-courts) by Max Rabin.\n",
"\n",
"We aim to solve the wave equation:\n",
"$$ \\frac{\\partial^2 p}{\\partial t^2} = c^2 \\nabla^2 p $$\n",
"where $p$ denotes the over pressure, and $c$ the speed of sound, all\n",
"inside a 2D box of size 20' by 40' (the offical racquetball [court dimensions](http://learnracquetball.com/articles/court-dimensions.html)).\n",
"\n",
"This gives us a partial differential equation to solve, subject to boundary conditions that are supposed to represent the reflecting walls, for which we will use\n",
"\n",
"$$ \\nabla p \\cdot \\hat n = - c \\eta \\frac{\\partial p}{\\partial t} $$\n",
"Where the left hand side denotes the normal component of the gradient of our pressure field at a wall boundary, and the right is proportional to the time derivative of the pressure field at the wall."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# imports\n",
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib.pyplot as plt\n",
"import scipy.linalg as la\n",
"from scipy.interpolate import RectBivariateSpline\n",
"import numpy.polynomial.chebyshev as npcheb\n",
"import os, sys\n",
"from time import time\n",
"import base64\n",
"from IPython.display import clear_output, HTML, Audio, display, Image\n",
"from itertools import count\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 41
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Constants\n",
"c = 2*56.3 # in racketball widths / sec\n",
"eta = 1e-2 # our impedance parameter"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will do the simulation by representing our pressure field on a chebyshev grid for increased accuracy.\n",
"\n",
"This means the samples of our field are unequally spaced along the x and z direction, but this gives much\n",
"better convergence.\n",
"\n",
"In order to do so, we need to know what the sample points are and how to take derivatives on this lattice, for which we use the following utility function"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def chebdiff(N): \n",
" \"\"\" Return the sampling points and differentiation matrix for a \n",
" chebyshev polynomial interpolant of the specified size \"\"\"\n",
" if N==0: return 0.0 \n",
" x = npcheb.chebpts2(N+1)\n",
" c = (np.r_[2, np.ones(N-1), 2])*(-1)**(np.arange(N+1)) \n",
" dX = x[:,None] - x[None,:]\n",
" D = ( c[:,None]*(1./c[None,:]) )/( dX + np.eye(N+1) ) \n",
" D = D - np.diag(D.sum(1)) \n",
" return x, D "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we proceed to set up the simulation with some chosen parameters and initial conditions."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Simulation setup\n",
"Nx = Nz = 64\n",
"\n",
"ptsx, Dx = chebdiff(Nx-1)\n",
"ptsz, Dz = chebdiff(Nz-1)\n",
"ptsz = ptsz*2 + 2 # scale the z points to be from 0 to 4\n",
"Dz = Dz/2 # scale the derivative matrix to match this scaling\n",
"\n",
"# compute second derivative matrices\n",
"Dx2 = Dx.dot(Dx)\n",
"Dz2 = Dz.dot(Dz)\n",
"\n",
"# Extract the first and last rows of these matrices for convenience\n",
"Dxl = Dx[0]\n",
"Dxr = Dx[-1]\n",
"Dzl = Dz.T[:,0]\n",
"Dzr = Dz.T[:,-1]\n",
"\n",
"# Repeat the zs and xs into a two grid\n",
"zz,xx = np.meshgrid(ptsz,ptsx)\n",
"\n",
"rate = 44100 # sampling rate for sound\n",
"# set our stepsize to be OVERSTEP steps per sample\n",
"OVERSAMP = 1\n",
"dt = (1./rate)/(OVERSAMP + 0.)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# initial conditions for simulation\n",
"x0, z0 = 0.9, 0.1\n",
"# initial pressure is a gaussian centered at (x0, z0) of size sigma\n",
"sigma = 0.06\n",
"p = np.exp(-((xx - x0)**2 + (zz - z0)**2)/(2*sigma**2))\n",
"# previous time step was a smaller version of this gaussian\n",
"tau = 0.01\n",
"pold = p * np.exp(-dt/tau)\n",
"# initial velocity field is just a first order estimate\n",
"v = (p-pold)/dt\n",
"# set the initial pressures and velocities on the walls to be zero\n",
"p[0,:] = p[-1,:] = 0\n",
"p[:,0] = p[:,-1] = 0\n",
"v[0,:] = v[-1,:] = 0\n",
"v[:,0] = v[:,-1] = 0"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since our function is defined on a chebyshev grid, in order to view it in its proper form, we need to do\n",
"a spline fit to this unequally spaced rectangular grid"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f = RectBivariateSpline(ptsx,ptsz, p) \n",
"xi,zi = np.ogrid[-1:1:100j, 0:4:200j]\n",
"\n",
"#setup nice figure for saving frames\n",
"fig = plt.figure(frameon=False)\n",
"fig.set_size_inches(6,3)\n",
"ax = plt.Axes(fig, [0.,0.,1.,1.])\n",
"ax.set_axis_off()\n",
"fig.add_axes(ax)\n",
"impic = ax.imshow( f(xi, zi), vmin=-0.1, vmax=0.1, aspect='auto', cmap=plt.cm.coolwarm)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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PEL9nTpOIntz43gksBZlBm0XPC0mG4a3kXMkjTvtnZmG3ek5lafv6YznUcF9M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\nAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x10d0d1d50>"
]
}
],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Create a directory to save our images to\n",
"try:\n",
" os.mkdir(\"/tmp/pics\")\n",
"except OSError:\n",
" print \"Directory already exists\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Directory already exists\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# our update equation calculator\n",
"def get_dp_dv(p,v):\n",
" \"\"\" Compute our updates given a p and v field \"\"\"\n",
" dp = np.zeros_like(v)\n",
" \n",
" # dp = v on the interior of the room\n",
" dp[1:-1,1:-1] = v[1:-1,1:-1]\n",
" # enfource the boundary conditions on the walls\n",
" dp[:,0] += c*eta*p.dot(Dzl)\n",
" dp[:,-1] += -c*eta*p.dot(Dzr)\n",
" dp[0,:] += c*eta*Dxl.dot(p)\n",
" dp[-1,:] += -c*eta*Dxr.dot(p)\n",
" \n",
" # wave equation dv = d2p = c^2 lapp (p)\n",
" dv = c**2 * (Dx2.dot(p) + p.dot(Dz2.T))\n",
" \n",
" # enforce boundary conditions\n",
" dv[:,0] += c*eta*v.dot(Dzl)\n",
" dv[:,-1] += -c*eta*v.dot(Dzr)\n",
" dv[0,:] += c*eta*Dxl.dot(v)\n",
" dv[-1,:] += -c*eta*Dxr.dot(v)\n",
"\n",
" return dp,dv"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"STEPS = int(2/dt) # simulate for 2 seconds\n",
"# set up lists to track conditions\n",
"pvals = [p.copy()]\n",
"vvals = [v.copy()]\n",
"\n",
"samplepoints = np.array([[13,-13],[13,32],[13,13],[32,-13],[32,32],[32,13],[-13,-13],[-13,32],[-13,13]])\n",
"sound = np.zeros((samplepoints.shape[0],STEPS))\n",
"\n",
"start_time = time()\n",
"imcounter = count(0)\n",
"# Actual simulation\n",
"for i in xrange(STEPS):\n",
"\n",
" # do RK4 update\n",
" dp1,dv1 = get_dp_dv(p,v)\n",
" dp2,dv2 = get_dp_dv(p+dt/2*dp1, v+dt/2*dv1)\n",
" dp3,dv3 = get_dp_dv(p+dt/2*dp2, v+dt/2*dv2)\n",
" dp4,dv4 = get_dp_dv(p+dt*dp3, v+dt*dv3)\n",
" p = p+dt/6 *( dp1 + 2*dp2 + 2*dp3 + dp4 )\n",
" v = v+dt/6 *( dv1 + 2*dv2 + 2*dv3 + dv4 )\n",
" \n",
" # save the sound as viewed at a particular coordinate on the grid\n",
" if i%OVERSAMP==0:\n",
" for j, loc in enumerate(samplepoints):\n",
" sound[j,i] = p[loc[0],loc[1]]\n",
" \n",
" # Progress\n",
" if i%(OVERSAMP*1000) == 0:\n",
" clear_output()\n",
" current_time = time()\n",
" print \"iter: {} progress: {:.3%} elapsed time: {:.0f}s est remaining: {:.0f}s\".format(i, \n",
" i/(STEPS+0.), current_time-start_time, (current_time-start_time)/(i+1) * (STEPS - i + 0.) )\n",
" sys.stdout.flush()\n",
" \n",
" # save output figures to /tmp/pics only every X samples\n",
" if i%(OVERSAMP*100) == 0:\n",
" pvals.append(p.copy())\n",
" f = RectBivariateSpline(ptsx,ptsz, p )\n",
" impic.set_data(f(xi,zi))\n",
" impic.figure.savefig(\"/tmp/pics/wave{:06d}.png\".format(imcounter.next()),dpi=50)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"iter: 88000 progress: 99.773% elapsed time: 88s est remaining: 0s\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Results"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# look at last step\n",
"f = RectBivariateSpline(ptsx,ptsz, pvals[0]) \n",
"impic.set_data(f(xi,zi))\n",
"fig"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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64H9CPyul1J1S5ZTPR38In2/xPtrb3rIriG979u7EpmNPjzJCxNjO7WNs+WHt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\nXr3f0/ufvaF3P3s/dppv3hJ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"prompt_number": 28,
"text": [
"<matplotlib.figure.Figure at 0x10d0d1210>"
]
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# make an mp4 of simulation\n",
"\n",
"#for mac\n",
"!ffmpeg -v warning -i /tmp/pics/wave%06d.png -tune stillimage -pix_fmt yuv420p -c:v libx264 -tune stillimage /tmp/bounce.mp4\n",
"\n",
"#for ubuntu\n",
"#!avconv -v warning -i /tmp/pics/wave%06d.png -tune stillimage -pix_fmt yuv420p -c:v libx264 -tune stillimage /tmp/bounce.mp4"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# embed the video in the ipython notebook\n",
"vidraw = base64.encodestring(open(\"/tmp/bounce.mp4\",\"rb\").read())\n",
"HTML(\"\"\"<video controls alt=\"test\" src=\"data:video/mp4;base64,{}\">\"\"\".format(vidraw))"
],
"language": "python",
"metadata": {},
"outputs": [
{
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