Instructables
A Flanger is an effects pedal that simulates two identical signals that are mixed together, but with one signal time-delayed by a small and gradually changing amount, usually smaller than 20 milliseconds. This was originally created using two tape decks but can now be done digitally using a free and open-source program called Audacity.
 
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Step 1: What You Will Need

Picture of What You Will Need

You will need:

A computer capable of running Audacity (Linux, Windows, or Mac)

Audacity

Dual Tape Decks Audacity Nyquist Plug-In (dualtapedecks.ny)

Stereo Butterfly (static) Audacity Nyquist Plug-In (buttrfly.ny)

A guitar recording (can be done in Audacity)

Step 2: Installing

Picture of Installing
Make sure Audacity is installed. Download Dual Tape Decks and Stereo Butterfly (static) from http://wiki.audacityteam.org/wiki/Download_Nyquist_Plug-ins.

Extract the .zip files and make sure that the nyquist file names are in lower case (eg. buttrfly.ny  NOT BUTTRFLY.NY)

Copy dualtapedecks.ny and buttrfly.ny into:
/usr/share/audacity/plug-ins/  if you use Linux
OR
C:/Program Files/Audacity/Plug-Ins if you use Windows

Step 4: Dual Tape Decks


Double-click to select the recording and then click Effect...Plugins 1 to ?...Dual Tape Decks.
I recommend using these settings:

LFO Frequency == 0.1 HZ
Starting Phase == 0 degrees
Phase Difference == 180 degrees
Depth == 0.01


Click OK to apply the effect.

Step 5: Stereo Butterfly (static)

Double-click to select the audio track. Click Effect...Plugins 1 to ?...Stereo Butterfly. Set stereo width to 0.00 and then click OK.

Step 6: Dual Tape Decks (Again)


Re-apply the Dual Tape Decks effect by double-clicking the track to select it then click on Effect...Plugins 1 to ?...Dual Tape Decks. Use the same settings as you used the first time in Step 4.

Step 7: Done

Your audio recording should now have a Flanging effect. You can now export it or add another layer to it. Have fun with this effect!

I have attached samples of this effect in MP3 and OGG formats. The OGG version will play directly in Firefox.