# Combining Two Manipulated Plots Dependent on Same Variables

I need to combine two plots on the same graph to highlight the intersection of the two while being able to manipulate various parameters that are common to both functions. I need to have the slider simultaneously change the parameters for each function and continue to plot on the same graph. Here's my code:

Manipulate[
right = Plot[Cos[2*Pi*b*n/\[Lambda]], {n, 0, 2}], {{a, 25,
"x-separation"}, 20, 30}, {{b, 25, "z-separation"}, 20,
30}, {{r, 1, "Rod Radius"}, .1,
10}, {{\[Lambda], 100, "Wavelength"}, 50, 200}]

Manipulate[
left = Plot[
Cos[2*Pi*
b/\[Lambda]] + (\[Lambda]*Sin[2*Pi*b/\[Lambda]])/(2 a*
Log[a/(2*Pi*r)]), {n, 0, 2}], {{a, 25, "x-separation"}, 20,
30}, {{b, 25, "z-separation"}, 20, 30}, {{r, 1, "Rod Radius"}, .1,
10}, {{\[Lambda], 100, "Wavelength"}, 50, 200}]

Show[right, left] // Dynamic


Any help is much appreciated!

Manipulate[
Plot[{Cos[2*Pi*b/λ] + (λ*Sin[2*Pi*b/λ])/(2 a*Log[a/(2*Pi*r)]),
Cos[2*Pi*b*n/λ]}, {n, 0, 2}],
{{a, 25, "x-separation"}, 20, 30}, {{b, 25, "z-separation"}, 20, 30},
{{r, 1, "Rod Radius"}, .1, 10}, {{λ, 100, "Wavelength"}, 50, 200}]


• Thanks for your help! I wasn't thinking to put the two functions inside Plot but this works much more efficiently than the other routes I've tried. Dec 9, 2013 at 5:51
• Thank you -- this is really helpful! I was trying to combine Manipulate with the Show commands and it simply wasn't working. This is very effective. Apr 13 at 16:33

Here is another simpler example that can compare how amplitude, frequency, and phase shift can impact the shape of a Sine function.

Manipulate[
Plot[{Sin[x], a Sin[k x + phi]}, {x, 0, 2 Pi}],
{k, .1, 4},{a, 1, 2}, {phi, 0, 2 Pi}
]