{"id":2861,"date":"2018-07-12T09:51:18","date_gmt":"2018-06-28T18:26:03","guid":{"rendered":"http:\/\/commons.princeton.edu\/josephhenry\/frequency-analysis\/"},"modified":"2018-07-12T09:51:18","modified_gmt":"2018-07-12T14:51:18","slug":"frequency-analysis","status":"publish","type":"page","link":"https:\/\/commons.princeton.edu\/josephhenry\/frequency-analysis\/","title":{"rendered":"Frequency analysis"},"content":{"rendered":"

Wave created by LC circuit<\/h3>\n

As we know, the basic physic model of oscillatory discharge is an LC circuit, whose resonance frequency is given by\u00a0\"\"\u00a0.\u00a0 Therefore by varying the length of wire loop used for discharge, we will be able to get waves of different frequency. Here we use single wire loops with length of 1m, 2m, 3m and 4m to discharge the same Leyden jar (the parameter of this Leyden jar can be found\u00a0here<\/a>).<\/p>\n

The inductance of the wire loop can be calculated by \"\", or\u00a0online calculator.<\/a><\/p>\n

Following is the calculated results and measured results. The resonance frequency is then calculated using C=1800pF:<\/p>\n\n\n\n\n\n\n\n
Loop size:<\/td>\nCalculated value(H)<\/td>\nFreq=1\/(2*PI*SQRT(LC)) (Hz)<\/td>\n<\/tr>\n
1m, R~=50cm, d=1mm<\/td>\n3.95467E-06<\/td>\n1886378.609<\/td>\n<\/tr>\n
2m, R~=60cm, d=1mm<\/td>\n4.88307E-06<\/td>\n1697608.166<\/td>\n<\/tr>\n
2m, R~=90cm, d=1mm<\/td>\n7.78317E-06<\/td>\n1344638.442<\/td>\n<\/tr>\n
3m, R~=120cm, d=1mm<\/td>\n1.08114E-05<\/td>\n1140888.843<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The setup is shown below:<\/p>\n

\"\"<\/p>\n

\n

Wave detection<\/h3>\n

The wave is detected using an oscilloscope with two short wires attached which function as an antenna:<\/p>\n

\"\"<\/p>\n

After the wave was captured by the oscilloscope, it was then saved to a USB and more analysis could be done using computer.<\/p>\n

Results<\/h3>\n

Below is a summary of the results. According to the equation for LC circuit, the theoretical\u00a0 ratio between two frequency equals to the square root of the ration of wire length. Click the links to view the waveforms and frequency analysis generated by different wire loops.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

length<\/p>\n<\/td>\n

Frequency(Hz)<\/td>\nAvg. Freq.(Hz)<\/td>\nRatio<\/td>\n\n

Theoretical ratio<\/p>\n<\/td>\n<\/tr>\n

1<\/td>\n1996805<\/p>\n

waveform<\/a><\/p>\n

frequency<\/a><\/td>\n

<\/td>\n1m \/ 2m: 1.240487734<\/td>\n<\/td>\n<\/tr>\n
1<\/td>\n2158556<\/p>\n

waveform<\/a><\/p>\n

frequency<\/a><\/td>\n

2077680.5<\/td>\n2m \/ 4m: 1.319149986<\/td>\n1:2==1.414213562<\/td>\n<\/tr>\n
2<\/td>\n1597444<\/p>\n

\u00a0waveform<\/a><\/p>\n

frequency<\/a><\/td>\n

<\/td>\n2m \/ 3m: 1.157499627<\/td>\n2:3==1.224744871<\/td>\n<\/tr>\n
2<\/td>\n1752336<\/p>\n

waveform\u00a0<\/a><\/p>\n

frequency<\/a><\/td>\n

1674890<\/td>\n3m \/ 4m: 1.139654783<\/td>\n3:4==1.154700538<\/td>\n<\/tr>\n
3<\/td>\n1484561<\/p>\n

waveform\u00a0<\/a><\/p>\n

frequency<\/a><\/td>\n

<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
3<\/td>\n1400000<\/p>\n

waveform<\/a><\/p>\n

frequency<\/a><\/td>\n

<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
3<\/td>\n1456408<\/p>\n

waveform<\/a><\/p>\n

frequency<\/a><\/td>\n

1446989.667<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
4<\/td>\n1366950<\/p>\n

waveform\u00a0<\/a><\/p>\n

frequency<\/a><\/td>\n

<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
4<\/td>\n1214575<\/p>\n

waveform<\/a><\/p>\n

frequency<\/a><\/td>\n

<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
4<\/td>\n1227496<\/p>\n

waveform\u00a0<\/a><\/p>\n

frequency<\/a><\/td>\n

1269673.667<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Wave created by LC circuit As we know, the basic physic model of oscillatory discharge is an LC circuit, whose resonance frequency is given by\u00a0\u00a0.\u00a0 Therefore by varying the length of wire loop used for discharge, we will be able to get waves of different frequency. Here we use single wire loops with length of … Continue reading “Frequency analysis”<\/span><\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-2861","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/pages\/2861","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/comments?post=2861"}],"version-history":[{"count":1,"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/pages\/2861\/revisions"}],"predecessor-version":[{"id":2888,"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/pages\/2861\/revisions\/2888"}],"wp:attachment":[{"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/media?parent=2861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/categories?post=2861"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/commons.princeton.edu\/josephhenry\/wp-json\/wp\/v2\/tags?post=2861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}