File:Retarded time.webm
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Size of this JPG preview of this WEBM file: 800 × 370 pixels. Other resolutions: 320 × 148 pixels | 874 × 404 pixels.
Original file (WebM audio/video file, VP8, length 23 s, 874 × 404 pixels, 547 kbps overall, file size: 1.52 MB)
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Summary
[edit]| Description |
English: Signals (e.g. light) move at a finite speed, so there is a time lag between when they are emitted and when they are detected. If the source is moving, the detector will "see" the signal that was emitted at a previous time, not the signal that is being emitted right now, and this time lag can change with time in a complicated way.
(Notice that, as the source is always moving slower than the signal, the detector sees the signals in the same order they were emitted.) |
| Date | |
| Source | https://mathstodon.xyz/@j_bertolotti/111346098723277032 |
| Author | Berto |
| Permission (Reusing this file) |
https://mathstodon.xyz/@j_bertolotti/111363365323269417 |
Mathematica 13.1 code
[edit]f[t_] := {Sin[2*2 \[Pi] t], Sin[2 \[Pi] t]}; p = {0, 1.2};
c = 15;
frames = Table[
tmp =
Table[Style[{tj, Norm[p - f[tj]]/c + tj }, Hue[tj]], {tj, -0.08, Min[t0, 0.6], 0.01}];
Grid[{{
ParametricPlot[f[t], {t, -0.08, 0.6}, PlotRange -> {{-1.5, 1.5}, {-0.5, 2.5}}, AspectRatio -> 1, PlotStyle -> {Thin, LightGray}, Axes -> False, Background -> Black, Epilog -> {Yellow, Disk[f[t0], 0.03], White, Disk[p, 0.03], Table[{Hue[tj], Circle[f[tj], c (t0 - tj)]}, {tj, -0.08, Min[t0, 0.6], 0.01}]}, ImageSize -> 300]
,
ListPlot[Select[tmp, (t0 >= #[[1, All]][[2]]) & ], Axes -> False, Frame -> True, PlotRange -> {{-0.1, 0.55}, {0, 0.68}}, FrameStyle -> Directive[Thick, White], Background -> Black, FrameTicks -> None, LabelStyle -> Medium, FrameLabel -> {"Time emitted", "Time detected"}, ImageSize -> 350]
}}, Background -> Black]
, {t0, -0.09, 0.61, 0.00201}];
ListAnimate[frames]
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:04, 6 November 2023 | 23 s, 874 × 404 (1.52 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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