{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Exploring Beat Frequencies using the `Audio` Object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This example uses the `Audio` object and Matplotlib to explore the phenomenon of beat frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interactive\n",
    "from IPython.display import Audio, display\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def beat_freq(f1=220.0, f2=224.0):\n",
    "    max_time = 3\n",
    "    rate = 8000\n",
    "    times = np.linspace(0,max_time,rate*max_time)\n",
    "    signal = np.sin(2*np.pi*f1*times) + np.sin(2*np.pi*f2*times)\n",
    "    display(Audio(data=signal, rate=rate))\n",
    "    return signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6add603d0359468d8311e567a4b28088"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = interactive(beat_freq, f1=(200.0,300.0), f2=(200.0,300.0))\n",
    "display(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'f1': 220.0, 'f2': 224.0}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.kwargs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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7XxnnMXN3Zk412Ga16DqDuXVQK4zo3ES1GI7EX/oHf4zskoBbB0leIH8Euku1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\nMRJLboR3b0hFxlPDbWkrOkp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e636588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f1, f2 = v.children[:2]\n",
    "f1.value = 255\n",
    "f2.value = 260\n",
    "plt.plot(v.result[0:6000]);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "05c9ddef84d641c7a88251736f6c6e53": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "jupyter-js-widgets",
       "_model_module_version": "~2.0.30",
       "_view_module": "jupyter-js-widgets",
       "_view_module_version": "~2.0.30",
       "layout": "IPY_MODEL_bac74f06cf2b49c3b3969c412d99c5ae",
       "msg_throttle": 1
      }
     },
     "354a6627a5e44c16a9bce0762abba93b": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "LayoutModel",
      "state": {
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30"
      }
     },
     "47eaf93e97b44fa59aace467f4ecbf90": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "LayoutModel",
      "state": {
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30"
      }
     },
     "6add603d0359468d8311e567a4b28088": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30",
       "children": [
        "IPY_MODEL_d0ce625176d542639b7af605a9e70aa9",
        "IPY_MODEL_8faaa532187041109c2458d109e1b529",
        "IPY_MODEL_05c9ddef84d641c7a88251736f6c6e53"
       ],
       "layout": "IPY_MODEL_354a6627a5e44c16a9bce0762abba93b"
      }
     },
     "8faaa532187041109c2458d109e1b529": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "FloatSliderModel",
      "state": {
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30",
       "description": "f2",
       "layout": "IPY_MODEL_47eaf93e97b44fa59aace467f4ecbf90",
       "max": 300,
       "min": 200,
       "step": 0.1,
       "value": 260
      }
     },
     "bac74f06cf2b49c3b3969c412d99c5ae": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "LayoutModel",
      "state": {
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30"
      }
     },
     "d0ce625176d542639b7af605a9e70aa9": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "FloatSliderModel",
      "state": {
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30",
       "description": "f1",
       "layout": "IPY_MODEL_e1710ea8c1394c37994d28b4c67e805a",
       "max": 300,
       "min": 200,
       "step": 0.1,
       "value": 255
      }
     },
     "e1710ea8c1394c37994d28b4c67e805a": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.0.30",
      "model_name": "LayoutModel",
      "state": {
       "_model_module_version": "~2.0.30",
       "_view_module_version": "~2.0.30"
      }
     }
    },
    "version_major": 1,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}