My teacher told me to hold the second step of waltz longer(ie: 1 22 3 - ie: natural turn). is that mean the third step has to speed up ?

I definatly in agreement with checking with your teacher on what exactly he is talking about. The second beat of Waltz is where most of movement occurs (Swing and Sway), and I would guess that ( one, Twooooo... three...) is trying to descibe swing and sway. Generally, a hover type movement is a help position with the feet rather close together... often held for a few bars. Unless your working on Open material, I wouldn't expect you to be working on "hover" movements.
If you look at what is happening, step one is where you collect and prepare for swing and sway. Remember, on the beat of one ( which is where the ACCENT is) you should have your weight into you knees,over your foot, preparing to move. Beat two is where SWING and SWAY occur, this is mearly a the release of the energy from your legs, which was prepared for on the privious step. On the third beat, a LOT of things happen. The feet close, this is where you are supposed to feel the highest point of rise. Next, you have to lower in a controlled manner, so that you don't apppear heavy, and sloppy. Also, let's not forget, before the next beat... the (&).. you have to extend, and change shape!!
As I see it, the hardest part of Waltz, and the most time consuming part.. is the third beat and the time between it and the next bar. One thing I was told by my coach to help with this.. is.. (Quick Quick Slow..)
What do you think about that??
This is mearly a way to "trick" yourself into really taking the time lower and extend into the next bar.
I really like this thought, before, I had been chanting, (1,2,3,&.. 1,2,3,&...)
Try it and see what you think.

In music it's known as "rubato".

Playing everything in perfectly strict time leads to a very mechanical robotic sound.

Classical musicians are famous for adding rubato in their playing. I've even heard some of my non classical friends say that classical musicians can't keep the beat because they are so used to altering the time as they play.

Regardless, rubato is one of those things that helps give music a sense of direction, movement and energy. It's the sense of rise and fall others are referring too. Interpretation.

You might think of the 2nd beat thing as a ball thrown into the air. There's a point where it's neither rising or falling. Now imagine the cartoon coyote of roadrunner fame. He fires off on a rocket chasing the roadrunner. At the high point he always seems to run out of fuel at the high point (apogee). As his rocket falls out from under him he struggles a bit to hover stealing a bit of time in the face of the inevitable. However, eventually he falls away and by Newton's Laws of Physics has to hit the ground at the same time as his spent rocket.

Whoa, what did I have for breakfast!

OB

Hovering on the second step certainly gives waltzing more character. My teacher recently asked me to start holding beat 2 for a fraction longer to give a hover effect. You do have to steal time from beat 3 (beat 1 in the backward turning lock?) but it's important to remember that it's only a fraction of a beat (less than half a beat)and the exact amount depends on your interpretation - this is what dancing is all about after all. You should normally be perfectly balanced at the end of beat 2- the step on beat 3 is a 'gethering' step to prepare you for the next power step on beat 1. Check your balance by dancing slowly - without music. This will uncover a lot of problems!!

You must be careful if you are emphasizing the two not to take so much time that you rush through "3." Rushing through "3" will force you to either lower too quickly or lower through "1."

Blair

It's called "hovering" when you lengthen the second step. Two should be the longest (widest) step, the highest step, and the timing should be extended. If you have the proper "fall," Three will not appear or feel rushed. You should look like you're floating outside of time before moving on. It would be counted "One, Twoooooo, Three." hee-hee! I was just saying that out loud as I was typing it. Hope this helps!

another LB