I'm trying to use the frequency analysis tool in Cool Edit Pro.

It seems the spectrum it gives you is dependent on where you place the
cursor.

Where do I have to put the cursor to get a correct spectral analysis of
the whole wave?

If I put it at the beginning of the wave, the frequency analysis looks
plausible.

If I put it at the end of the wave, the frequency analysis still looks
plausible but is different.