The Doppler Effect
Author
Senan Sekhon
Last Updated
2 years ago
License
Creative Commons CC BY 4.0
Abstract
Graphic illustrating the Doppler effect with radar speed detection, created in TikZ
\documentclass[10pt]{extarticle}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[dvipsnames]{xcolor}
\usepackage[utf8]{inputenc}
\usepackage[paperwidth=14cm,paperheight=7.5cm,top=0.5cm,bottom=0.5cm,left=0.5cm,right=0.5cm]{geometry}
\usepackage{tikz,tikzpeople}
\usetikzlibrary{arrows}
\usepackage[most]{tcolorbox}
%Defining a command for a sine wave joining two points
%\wave[options]{x-coordinate of initial point}{y-coordinate of initial point}{x-coordinate of final point}{y-coordinate of final point}{frequency}{amplitude}
\newcommand{\wave}[7][]{
%\fill[red] (#2,#3) circle (1pt) node[right]{i}; %initial point (for visual aid)
%\fill[blue] (#4,#5) circle (1pt) node[right]{f}; %final point (for visual aid)
\pgfmathsetmacro{\len}{sqrt((#4-#2)^2+(#5-#3)^2)} %length of line joining
\pgfmathsetmacro{\angle}{atan2(#5-#3,#4-#2)}
\begin{scope}[shift={(#2,#3)},rotate=\angle,xscale=\len,yscale=#7] %Transformations MUST be in this order to render properly!
\draw[#1] plot[domain=0:1,smooth,samples=300] (\x,{sin(2*pi*#6*deg(\x))}); %the wave
\end{scope}}
%Created by Senan Sekhon
%September 3, 2021
\begin{document}
\definecolor{boxcol}{HTML}{031769} %Box color
\begin{center}
\begin{tcolorbox}[title=The Doppler Effect, fonttitle=\large\sffamily\bfseries\itshape\selectfont,halign title=center,colback=white,colframe=boxcol,coltitle=white,top=0pt,bottom=0pt,left=0pt,right=0pt,toptitle=1pt,bottomtitle=1pt,boxsep=0pt,arc=2mm,hbox]
\begin{tikzpicture}
\clip (-7,-2.6) rectangle (5,2.8);
%\draw (-7,-2.6) rectangle (5,2.8); %Border (optional)
\begin{scope}[scale=1] %Road
\shade[left color=green!10!gray!40!black,right color=green!10!gray!40!black,middle color=green!20!gray!20!black] (-7,-0.5) rectangle (5,0.5); %The road
\foreach \a in {-6,-3,0,3} %lane dividers
\fill[white] (\a-0.3,-0.03) rectangle (\a+0.3,0.03);
\end{scope}
\draw[fill=Cerulean!20,rounded corners=0.4mm] (1.1,0.8)--(1.6,1.1)--(1.7,1.1)--(1.2,0.8); %windshield
\begin{scope}[even odd rule] %Chassis
\clip (0,0) rectangle (6,2) (1,0.3) circle (.35) (3.7,0.3) circle (.35); %clipping wheel cavities out of chassis
\definecolor{fcol}{HTML}{AD5389} %front color
\definecolor{rcol}{HTML}{3C1053} %rear color
\shadedraw[draw=black,left color=fcol,right color=rcol,shading angle=135,rounded corners=2mm] (0.2,0.2)--(0,0.6)--(0.8,0.8)--(1.4,0.8) arc(-105:-75:4)--++(15:0.4) arc(105:60:1.2)--(4.5,0.2)--cycle; %The chassis
\end{scope}
\begin{scope} %Visual aesthetics for the front wheel
\clip (0.6,0.2) rectangle (1.4,0.7);
\draw (1,0.3) circle (.35); %chassis cavity border for front wheel
\clip (0.6,0.25) rectangle (1.4,0.7);
\fill[black] (1,0.3) circle (.35); %dark background behind front wheel
\end{scope}
\begin{scope} %Visual aesthetics for the rear wheel
\clip (3.3,0.2) rectangle (4.1,0.7);
\draw (3.7,0.3) circle (.35); %chassis cavity border for rear wheel
\clip (3.3,0.25) rectangle (4.1,0.7);
\fill[black] (3.7,0.3) circle (.35); %dark background behind rear wheel
\end{scope}
%Front and rear wheels
\fill[gray!50!black] (1,0.3) circle (.3); %front wheel - outer portion
\fill[gray!50!black] (3.7,0.3) circle (.3); %rear wheel - outer portion
\fill[gray!80] (1,0.3) circle (.2); %front wheel - inner portion
\fill[gray!80] (3.7,0.3) circle (.2); %rear wheel - inner portion
\draw[{Latex[scale=0.8]}-,thick] (1.2,-0.7)--(3.5,-0.7) node[scale=1.25,midway,below]{$v$}; %arrow for velocity of car
\begin{scope} %Driver
\clip (1.4,0.793) arc(-105:-75:4)--(2.7,1.6)--(2.3,1.6)--cycle; %clipping driver profile to 'fit' the chassis
\definecolor{scol}{HTML}{19022E} %shirt (blazer) color
\definecolor{ucol}{HTML}{F5C9EF} %undershirt color
\definecolor{tcol}{HTML}{350340} %tie color
\node[name=driver,scale=2,businessman,saturated,mirrored,hair=black,shirt=scol,undershirt=ucol,tie=tcol,monogramtext=\ ] at (2.4,1) {}; %The driver
\end{scope}
%Police officer
\definecolor{pcol}{HTML}{0408A6} %jacket and hat color
\node[name=police,scale=2,police,saturated,hair=black,shirt=pcol,hat=pcol] at (-6,1.6) {}; %The police officer
%%% Waves
%\draw (-5.4,2)--(1,1.6);
%\draw (-5.4,1.5)--(1,1.1);
\wave[-{Latex[scale=0.5]},red]{-5.4}{2}{1}{1.6}{4}{0.2}
\wave[{Latex[scale=0.5]}-,blue]{-5.4}{1.5}{1}{1.1}{8}{0.2}
\path (-5.4,2.4)--(1,2) %labels for transmitted signal
node[midway,sloped,red,font=\sffamily]{transmitted signal}
node[pos=0.03,sloped,red,font=\sffamily] {$f_0$}
node[pos=0.97,sloped,red,font=\sffamily] {$f_1$};
\path (-5.4,1.1)--(1,0.7) %labels for received signal
node[midway,sloped,blue,font=\sffamily]{received signal}
node[pos=0.03,sloped,blue,font=\sffamily] {$f_2$}
node[pos=0.81,sloped,blue,font=\sffamily] {$f_1$};
%Equations for Doppler effect
\node[right,red!70!black,font=\sffamily] at (-6.8,-1) {Transmission: $\displaystyle f_1=\frac{c+v}{c}f_0$};
\node[right,blue!70!black,font=\sffamily] at (-6.8,-1.8) {Reception: $\displaystyle f_2=\frac{c}{c-v}f_1=\frac{c+v}{c-v}f_0$};
\node[right,red!50!blue!70!black,font=\sffamily\bfseries] at (-0.6,-1.8) {Speed detected: $\displaystyle v=\frac{f_2-f_0}{f_2+f_0}c$};
\end{tikzpicture}
\end{tcolorbox}
\end{center}
\end{document}