sin wave with changing frequency

Question

I'm trying to recreate this image of the EM spectrum:

Electromagnetic Spectrum

I would like to draw a sin/cos wave of changing frequency as in the picture.

So far I've been doing something extremely hacky but this less than ideal because I can't change the form of the wave without manually going through and changing all the numbers. Can anyone suggest a more elegant solution that perhaps uses a single sine/cosine function?

\begin{tikzpicture}
\draw (0,0) -- (12,0);
\draw (0.2,1)node[left,font=\tiny] {$y=1$} -- (11.8,1);
\draw (0.2,-1)node[left,font=\tiny] {$y=-1$} -- (11.8,-1); 
\foreach \x in {0,0.5,...,12}{
\draw (\x,-0.2)node [below,font=\tiny,] {\x} -- (\x,0.2) ;
}
\draw[ultra thick, red] (0,0) sin (1,1);    %% the real business in this line
\draw[ultra thick, red] (1,1) cos (2.0,0);    %% the real business in this line
\draw[ultra thick, red] (2.0,0) sin (3,-1);    %% the real business in this line
\draw[ultra thick, red] (3,-1) cos (3.9,0);    %% the real business in this line
\draw[ultra thick, red] (3.9,0)  sin (4.8,1);    %% the real business in this line
\draw[ultra thick, red] (4.8,1) cos (5.6,0);    %% the real business in this line
\draw[ultra thick, red] (5.6,0) sin (6.4,-1);    %% the real business in this line
\draw[ultra thick, red] (6.4,-1) cos (7.2,0);    

 \draw[ultra thick, red] (7.2,0)  sin (7.9,1);    %% the real business in this line
\draw[ultra thick, red] (7.9,1) cos (8.55,0);    %% the real business in this line
\draw[ultra thick, red] (8.55,0) sin (9.2,-1);    %% the real business in this line
\draw[ultra thick, red] (9.2,-1) cos (9.7,0.0);

     \draw[ultra thick, red] (9.7,0)  sin (10.2,1);    %% the real business in this line
\draw[ultra thick, red] (10.2,1) cos (10.6,0);    %% the real business in this line
\draw[ultra thick, red] (10.6,0) sin (11.0,-1);    %% the real business in this line
\draw[ultra thick, red] (11.0,-1) cos (11.3,0); %% the real business in this line 

         \draw[ultra thick, red] (11.3,0)  sin (11.6,1);    %% the real business in this line
\draw[ultra thick, red] (11.6,1) cos (11.8,0);    %% the real business in this line
\draw[ultra thick, red] (11.8,0) sin (12.0,-1);    %% the real business in this line
\draw[ultra thick, red] (12.0,-1) cos (12.2,0); %% the real business in this line 

             \draw[ultra thick, red] (12.2,0)  sin (12.4,1);    %% the real business in this line
\draw[ultra thick, red] (12.4,1) cos (12.55,0);    %% the real business in this line
\draw[ultra thick, red] (12.55,0) sin (12.7,-1);    %% the real business in this line
\draw[ultra thick, red] (12.7,-1) cos (12.85,0); %% the real business in this line 

                 \draw[ultra thick, red] (12.85,0)  sin (13.0,1);    %% the real business in this line
\draw[ultra thick, red] (13.0,1) cos (13.1,0);    %% the real business in this line
\draw[ultra thick, red] (13.1,0) sin (13.2,-1);    %% the real business in this line
\draw[ultra thick, red] (13.2,-1) cos (13.3,0); %% the real business in this line 

 \draw[ultra thick, red] (13.3,0)  sin (13.4,1);    %% the real business in this line
\draw[ultra thick, red] (13.4,1) cos (13.48,0);    %% the real business in this line
\draw[ultra thick, red] (13.48,0) sin (13.56,-1);    %% the real business in this line
\draw[ultra thick, red] (13.56,-1) cos (13.62,0); %% the real business in this line 

     \draw[ultra thick, red] (13.62,0)  sin (13.69,1);    %% the real business in this line
\draw[ultra thick, red] (13.69,1) cos (13.76,0);    %% the real business in this line
\draw[ultra thick, red] (13.76,0) sin (13.82,-1);    %% the real business in this line
\draw[ultra thick, red] (13.82,-1) cos (13.88,0); %% the real business in this line 
\draw[ultra thick, red] (13.88,0)  sin (13.92,1);    %% the real business in this line
\end{tikzpicture}

Answer 1

With blueshift.

\documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[hide axis,red,width=16cm,height=4cm,thick] 
\addplot[domain=20:300,samples=800,        
colormap={}{ % Define the colormap from https://tex.stackexchange.com/questions/243689/create-a-plot-line-with-a-gradient
            color(2cm)=(red);
            color(16cm)=(blue);
        },
        ultra thick, point meta=x*x,mesh]{sin(pow(x,2)/15)};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

A sine wave with increasing frequency has the expression sin(deg((\fmin+\x*((\fmax-\fmin))/\xmax)*\x)) if the frequency increase is linear, and sin(deg(exp(ln(\fmin)+\x/\xmax*(ln(\fmax)-ln(\fmin)))*\x)) if the frequency increase is exponential. I have seen that the exponential increase seems to provide better looking results. In the following code, set \xmax to the maximum value of x, \fmin to the minimum frequency, and \fmax to the maximum frequency. The commented line uses linear frequency increase, and the uncommented line uses exponential frequency increase.

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}

\begin{document}
    \newcommand{\xmax}{14}
    \newcommand{\fmin}{(pi/3)}
    \newcommand{\fmax}{(2*pi)}
\begin{tikzpicture}[domain=0:\xmax, samples=500]
\draw (0,0) -- (12,0);
\draw (0.2,1)node[left,font=\tiny] {$y=1$} -- (11.8,1);
\draw (0.2,-1)node[left,font=\tiny] {$y=-1$} -- (11.8,-1); 
\foreach \x in {0,0.5,...,12}{
    \draw (\x,-0.2)node [below,font=\tiny,] {\x} -- (\x,0.2) ;
}

% The following line uses linear frequency increase
%\draw[ultra thick, red] plot (\x, {sin(deg((\fmin+\x*((\fmax-\fmin))/\xmax)*\x))} );
% The following line uses exponential frequency increase
\draw[ultra thick, red] plot (\x, {sin(deg(exp(ln(\fmin)+\x/\xmax*(ln(\fmax)-ln(\fmin)))*\x))} );

\end{tikzpicture}
\end{document}

Answer 3

A PSTricks solution only for comparison purposes.

\documentclass[pstricks]{standalone}
\usepackage{pst-plot,pst-calculate}
\begin{document}
\begin{pspicture}[algebraic](0,-1.5)(\pscalculate{2*pi},1.5)
    \psplot[plotpoints=3000]{0}{2 Pi mul}{sin(x^3/2)}
\end{pspicture}
\end{document}

Flipped version

\documentclass[pstricks]{standalone}
\usepackage{pst-plot,pst-calculate}
\begin{document}
\begin{pspicture}[algebraic](0,-1.5)(\pscalculate{2*pi},1.5)
    \psplot[plotpoints=3000]{0}{2 Pi mul}{sin((x-TwoPi)^3/2)}
\end{pspicture}
\end{document}