Research website of Vyacheslav Gorchilin
Standing waves in long lines. Animation
Harmonics — 1..5
Their phase: -90..0..+90
L
Q
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The standing waves in the long lines resemble a rope tied from one end and rocking with the other. If the frequency of excitation corresponds to the half wavelength, we will get in the middle of the rope is maximum (antinode) and at the ends a minimum (node). If the rope will be twice longer, at the same frequency for the excitation we get two antinodes and three nodes. Etc. — in the case of tied from one end of the rope we are going to get standing waves under the condition L*N/2, where L is the length of the ropes N are integers greater than zero.

If the frequency of excitation will correspond to a quarter wave length the situation will be quite different. Here for example it is better to take a long stick, the other end of which is free, which is what we need to experience. In this scenario, we get the node at the beginning of the stick where we got it and rocking, and the antinode is at the other end. Standing waves we obtain under the condition L*(N*2-1)/4.

But the most interesting pattern of standing waves is obtained if our stick or a rope to swing not only the fundamental frequency, but a sum of harmonics. This page allows you to carry out such experiments in online. Just select the sliders necessary harmonics, and their phases, the q line and the ratio of the wavelength, then click on the "Recalculate" button and immediately see the result. For example, you can get waves in a long line of excited quasi-rectangular, quasi-triangular or quasi saw-tooth pulses.

Axis — top to bottom delayed time schedule and a long swinging line fluctuations; it is obtained by simple summation of harmonics. Axis — left to right — our long line, where L is its total length. The buttons below the graph it can be overload, speed up, slow down and stop. These buttons and the slider of the q-factor change schedule without reloading the page — without clicking the "Recalculate" button.

As you can see a standing wave in a real inductor , see here.