As you realised, the problem is that the clip you are pasting in is of a lower sample rate (e.g. Frequency: 11 025 Hz as displayed on its Track Panel where the mute/solo buttons are) than the clip you are pasting into (e.g. 44 100 Hz).

The clip you are pasting in would in the example I have given be compressed to /4 of its original length and play four times as fast, because of its frequency disparity inside the track you have pasted it into.

To get round this situation where you are pasting a clip of one sample rate into a track with a different sample rate:

1) set the Project Rate button (at bottom left of the screen) to the rate of the track into which you want to paste

2) click in the Track Panel of the track you want to paste in (so as to select all of it), then Project > Quick Mix.

Now the track you just Quick Mixed will be resampled to the rate of the track you want to paste into, with the length and tempo remaining the same, so you can cut or copy and paste between them without problem.

Note the resampled track will have silence added to the end of it due to a current resampling bug, but you can simply select and delete the surplus silence.

However in our Audacity Beta version (currently 1.3.2) you can cut and paste between tracks of different sample rates and the pasted in track will be automatically resampled without the need for the user to do anything. This improvement will be incorporated into the next major stable release (1.4.0, possibly later this year).