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   "source": [
    "In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency $f$ and emitted frequency $f_\\text{0}$ is given by\n",
    "\\begin{equation}\n",
    "f = \\left( \\frac{c + v_\\text{r}}{c + v_\\text{s}} \\right) f_0 \\,\n",
    "\\end{equation}\n",
    "here\n",
    "* $c \\;$ is the velocity of waves in the medium;\n",
    "* $v_\\text{r} \\,$ is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);\n",
    "* $v_\\text{s} \\,$ is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).\n",
    "\n",
    "The frequency is decreased if either is moving away from the other."
   ]
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  {
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   "execution_count": 3,
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   "source": [
    "def f(c,vr,vs,f0):\n",
    "    return ((c + vr) / (c + vs)) * f0 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the ambulance is approaching you"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
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       "743.3168316831684"
      ]
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=343.2\n",
    "vr=0\n",
    "vs=-20\n",
    "f0=700\n",
    "f(c,vr,vs,f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the ambulance is driving away from you"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "661.453744493392"
      ]
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     "execution_count": 6,
     "metadata": {},
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   "source": [
    "c=343.2\n",
    "vr=0\n",
    "vs=20\n",
    "f0=700\n",
    "f(c,vr,vs,f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are approaching the ambulance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "740.7925407925408"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=343.2\n",
    "vr=20\n",
    "vs=0\n",
    "f0=700\n",
    "f(c,vr,vs,f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are running away from the police car"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "659.2074592074592"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=343.2\n",
    "vr=-20\n",
    "vs=0\n",
    "f0=700\n",
    "f(c,vr,vs,f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If nothing is moving "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "700.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=343.2\n",
    "vr=0\n",
    "vs=0\n",
    "f0=700\n",
    "f(c,vr,vs,f0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": true
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   "source": []
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