This happens when the record speed (say, 11,025 Hz) is different from the default playback speed (say, 22,050 Hz). When the same data is played back at double speed, the sound plays twice as fast and sounds twice as high, leading to the standard "chipmunk" effect. If you go to 44,100 you'll get four times as high/fast.
A common cause for this is the Audacity project Hz setting is different from the setting that you are recording at. .Wav files get stamped with a particular frequency when they are saved, and so always play back at that frequency with all standard players. The Audacity project frequency is found in a small white window in the lower-left-hand corner of Audacity's window. Check that this is appropriate for what you think you're doing.
You can save existing files at a different frequency to save them.
Resampling turns a file from one frequency/speed into a different frequency/speed without changing its apparent sound. In this case, you don't want to resample, as the data is correct but the sound (speed) is wrong, not vice versa.
If this happens in recording and not simply playing back outside of Audacity, then you've got a problem with the default recording speed of your PC somehow not writing into .wav files.