LaTeXのTikZ 〜波の干渉

波の干渉のための図を残しておく。

1. 必要なパッケージ

\usepackage{tikz}
\usepackage[dvipsnames]{xcolor}

色を変えるために xcolor パッケージを使う。また、NavyBlue や Maroon などの色を使っているので、 [dvipsnames] オプションを追加している。

2. 同位相の波源による波面

2-1. TikZ のコード

%波の干渉 作図用
\begin{tikzpicture}[baseline=0]
  \coordinate (A) at (-3.2,0); %x軸最小
  \coordinate (B) at (3.2,0); %x軸最小
  \node[left,scale = 1.5 ] at (A) {$S_1$};
  \node[right,scale = 1.5 ] at (B) {$S_2$};

  \begin{scope} \clip (-6,-3.6) rectangle (6,3.6);  
    \foreach \n in{0,1,...,10}
    {
    \draw[NavyBlue,semithick] (A) circle ( 1.2*\n) ;
    \draw[dashed,NavyBlue,semithick] (A) circle ( 1.2*\n + 0.6) ;
    \draw[Maroon,semithick] (B) circle ( 1.2 * \n) ;
    \draw[dashed,Maroon,semithick] (B) circle ( 1.2 * \n + 0.6) ;
      };
    \fill (A) circle ( 0.08) ;
    \fill (B) circle ( 0.08) ;
  
  \end{scope}
\end{tikzpicture} 

2-2. 出力の様子

実線は山を、破線は谷を示すつもりで記載した。

3. 同位相の波源による干渉が描く双曲線

3-1. TikZ のコード

% 双曲線を描画するマクロ
\newcommand{\drawHyperbola}[4]{
  \draw[very thick,samples=200,domain=#1:#2,gray!60,#4] plot(\x,{#3*sqrt(pow(\x,2)/pow(#1-0.00001,2) - 1) });
  \draw[very thick,samples=200,domain=#1:#2,gray!60,#4] plot(\x,{-#3*sqrt(pow(\x,2)/pow(#1-0.00001,2) - 1) });
  \draw[very thick,samples=200,domain=-#1:-#2,gray!60,#4] plot(\x,{#3*sqrt(pow(\x,2)/pow(#1-0.00001,2) - 1) });
  \draw[very thick,samples=200,domain=-#1:-#2,gray!60,#4] plot(\x,{-#3*sqrt(pow(\x,2)/pow(#1-0.00001,2) - 1) });
}
\begin{tikzpicture}[baseline=0, scale=1.0]
  \coordinate (A) at (-3.2,0); % 波源 S1 の位置
  \coordinate (B) at (3.2,0);  % 波源 S2 の位置
  \node[left,scale=1.5] at (A) {$S_1$};
  \node[right,scale=1.5] at (B) {$S_2$};

  \begin{scope}
    \clip (-7,-4) rectangle (7,4);  
    \foreach \n in {0,1,...,10} {
      \draw[NavyBlue,semithick] (A) circle (1.2*\n);
      \draw[dashed,NavyBlue,semithick] (A) circle (1.2*\n + 0.6);
      \draw[Maroon,semithick] (B) circle (1.2*\n);
      \draw[dashed,Maroon,semithick] (B) circle (1.2*\n + 0.6);
    }
    \fill (A) circle (0.1);  % 波源のサイズを少し大きく
    \fill (B) circle (0.1);

    %-------双曲線-------%
    \draw[very thick,gray!60] (0,10) -- ( 0,-10);

    \drawHyperbola{0.3}{6}{3.2}{dashed};
      \draw[very thick,gray!60,dashed] (0.3, 0.3) -- (0.3, -0.3);
      \draw[very thick,gray!60,dashed] (-0.3, 0.3) -- (-0.3, -0.3);
    \drawHyperbola{0.6}{6}{3.12}{};
      \draw[very thick,gray!60] (0.6, 0.1) -- (0.6, -0.1);
      \draw[very thick,gray!60] (-0.6, 0.1) -- (-0.6, -0.1);
    \drawHyperbola{0.9}{6}{3}{dashed};
      \draw[very thick,gray!60,dashed] (0.9, 0.1) -- (0.9, -0.1);
      \draw[very thick,gray!60,dashed] (-0.9, 0.1) -- (-0.9, -0.1);
    \drawHyperbola{1.2}{6}{2.96}{};
    \drawHyperbola{1.5}{6}{2.8}{dashed};
    \drawHyperbola{1.8}{6}{2.65}{};
    \drawHyperbola{2.1}{6}{2.4}{dashed};
    \drawHyperbola{2.4}{6}{2.1}{};
    \drawHyperbola{2.7}{6}{1.7}{dashed};


    \coordinate (P) at (1.8,3.3); %x軸最小
    \node[right,scale = 1.5 ] at (P) {P};
    \fill (P) circle ( 0.08) ;

    \draw[thick] (P) -- (A);
    \draw[thick] (P) -- (B);
    \node[scale = 1.5 ] at (0,2.4) {$l_1$};
    \node[scale = 1.5 ] at (2.7,2) {$l_2$};

    \draw[thick, Stealth-Stealth] (-4.4,0) -- (-5.6,0);
    \node[scale = 1.5 ] at (-5.0,-0.3) {$\lambda$};
  \end{scope}

  %強め合いを示す 双曲線 の インデックス
  \draw[thick, ->] (0, 3.8) -- (0,3.6);
  \node[scale = 1.0] at ( 0, 4 ) { $ m = 0$} ;
  %
  \draw[thick, ->] (-1, 3.8) -- (-0.95,3.6);
  \node[scale = 1.0] at ( -1, 4 ) { $ m = 1$} ;
  %
  \draw[thick, ->] (1, 3.8) -- (0.95,3.6);
  \node[scale = 1.0] at ( 1, 4 ) { $ m = 1$} ;
  %
  %弱め合いを示す 双曲線 の インデックス
  \draw[thick, ->] (0.5, -3.8) -- (0.45,-3.6);
  \node[scale = 1.0] at ( 0.5, -4 ) { $ m = 0$} ;
  %
  \draw[thick, ->] (-0.5, -3.8) -- (-0.45,-3.6);
  \node[scale = 1.0] at ( -0.5, -4 ) { $ m = 0$} ;
  %
  \draw[thick, ->] (1.5, -3.8) -- (1.4,-3.6);
  \node[scale = 1.0] at ( -1.5, -4 ) { $ m = 1$} ;
  %
  \draw[thick, ->] (-1.5, -3.8) -- (-1.4,-3.6);
  \node[scale = 1.0] at ( 1.5, -4 ) { $ m = 1$} ;
\end{tikzpicture}

3-2. 出力の様子