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Frequency analysis

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 \omega_0 =   {1 \over \sqrt{LC}}.  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 here).

The inductance of the wire loop can be calculated by " />, or online calculator.

Following is the calculated results and measured results. The resonance frequency is then calculated using C=1800pF:

Loop size:

Calculated value(H)

Freq=1/(2*PI*SQRT(LC)) (Hz)

1m, R~=50cm, d=1mm

3.95467E-06

1886378.609

2m, R~=60cm, d=1mm

4.88307E-06

1697608.166

2m, R~=90cm, d=1mm

7.78317E-06

1344638.442

3m, R~=120cm, d=1mm

1.08114E-05

1140888.843

The setup is shown below:


Wave detection

The wave is detected using an oscilloscope with two short wires attached which function as an antenna:


After the wave was captured by the oscilloscope, it was then saved to a USB and more analysis could be done using computer.

Results

Below is a summary of the results. According to the equation for LC circuit, the theoretical  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.

length

Frequency(Hz)

Avg. Freq.(Hz)

Ratio

Theoretical ratio

1

1996805

waveform 

frequency

 

1m / 2m: 1.240487734

 

1

2158556

waveform  

frequency

2077680.5

2m / 4m: 1.319149986

1:2==1.414213562

2

1597444

 waveform  

frequency

 

2m / 3m: 1.157499627

2:3==1.224744871

2

1752336 

waveform  

frequency

1674890

3m / 4m: 1.139654783

3:4==1.154700538

3

1484561

waveform  

frequency

     

3

1400000

waveform  

frequency

     

3

1456408

waveform  

frequency

1446989.667

   

4

1366950

waveform  

frequency

     

4

1214575

waveform  

frequency

     

4

1227496

waveform  

frequency

1269673.667