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October 24, 2016 00:41
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{ | |
"cells": [ | |
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"cell_type": "markdown", | |
"metadata": {}, | |
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"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." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"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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"data": { | |
"text/plain": [ | |
"743.3168316831684" | |
] | |
}, | |
"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 | |
}, | |
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{ | |
"data": { | |
"text/plain": [ | |
"661.453744493392" | |
] | |
}, | |
"execution_count": 6, | |
"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": [ | |
"You are approaching the ambulance" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"collapsed": false | |
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{ | |
"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", | |
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"metadata": { | |
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