Distorted sound on speakers

What would be the main cause?
I've had experienced a few occasions of distorted or strained sound on my speakers. One time, it was due to loose connection on the banana connection. After the connection is secured the problem was gone.

This time, all connections are fine, but one of my speakers are producing distorted sound on certain albums, mostly on CDs. More apparent on high frequency (high female soprano), but sometimes low keys on piano. It rarely suffers problems on LPs. I switched the speaker location (left to right and right to left), but the distorted sound is always on that particular speaker.
It is not only due to high volume. Evan mid volume on certain CDs produce distorted sound. I tried all my 3 CD players, but the result is the same.

Strange thing is that it is fine on certain other CDs.

Can I safely assume that the speaker is flawed?
It does sound like you fried a tweeter - this is common. Either your amp clipped and you damaged it or you speakers are not powerful enough to handle the listening levels you like.
I have two amps. 100WPC solid state power amp and 55WPC tube int amp. The speakers suffer the same problem with both amps.

Assuming the tweeter is fried, would it be an easy fix?
Assuming the tweeter is fried, would it be an easy fix?

Assuming this is the issue and you can find an exact replacement then it may cost no more than $50 depending on the speaker.

You may also want to check the woofer though - this kind of sound can also come from a voice coil rubbing in the woofer...

If you have time - swap the tweeters between the speakers and check again to see if the problem moves with the tweeter...
Yep, I think you have a bad tweeter. Solo piano is probably the best music to reveal a defective tweeter. I had a bad tweeter last year and the only time I would ever notice it was during solo piano. Once I replaced it, everything sounded better.
Right. The solo piano music reveals the problem very well.
Replacing/Swapping tweeters/woofers -- are they supposed to be an easy and safe job, even for those who are goofy in taking into parts and putting into a whole?

I will first try to swap the tweeters and see what happens.