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}

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}

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}

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}