Can I shorten the resonant length of a tight wire by moving its endpoint in phase? A stretched string, tube or wireless antenna has a resonance fixed by the velocity of the wave  (sound in air, metal, electrical wave etc.) and the length of the object. The fundamental occurs when a standing wave is anchored between points of mechanical or electrical constraint, such as the ends of the wire or tube.
If I were to move one of the fixed supports (an end of the string) such that it moves as if it were a point a few cm from the end of a standing wave of lower frequency, would it still resonate?
I think that it wouldn't, but I don't understand why. Do I need a more complex motion that also stretches the wire at 90 degrees phase shift from the movement?
 A: If I understand you correctly, you want to know what happens when you move one end of a string. Actually this is usually the way you get your standing wave in the first place. Mathematically, you can get the behavior by assuming a time dependent boudary condition at one end, e.g. a $\vec A_0\sin{\omega t}$ time dependence of the amplitude in a certain direction. Then, for transverse $\vec A_0$, you will get resonances (standing waves) for angular frequencies corresponding to integer multiples of a half wavelength + a quarter wavelength fitting into the length of the string. For longitudinal $\vec A_0$, you will get resonances for angular frequencies corresponding to integer multiples of a half wavelength.
If you have a string oscillating in a standing wave you can quench the oscillation by starting a (longitudinal) sinusoid oscillation with the standing wave frequency at an end point in anti-phase.  
A: Revised Answer (for earlier version click on "edited ... ago")
Reading your question as well as your comments it is still not quite clear what you mean.
I presume that the string of length $L$ with fixed ends A and B is set vibrating, as in the 1st figure below. The tension and mass per unit length determine the speed $v$ of travelling waves. The fundamental frequency is $f=\frac{2v}{L}$ (which comes from speed = wavelength x frequency). 
P is a point on the string close to end B. It vibrates with frequency $f$. Note that if we force P to vibrate with frequency $f$ then it does not matter whether or not the section PB of the string exists : we could remove it without destroying the standing wave. 

With the string at rest end B is then unfixed and forced to vibrate with the same motion that point P had in the 1st diagram. We now have the situation in the 2nd diagram.
If the moving end B has the same frequency $f$ as P, then a standing wave will not be formed on the string. The forcing frequency corresponds to a string of shorter length $L$, but the effective length $L'$ is now somewhat longer than $L$. (How much longer is difficult to say; see the discussion below.) The forcing frequency $f'$ should be correspondingly lower. The tension in the string and its mass per unit length are the same; the speed $v$ of waves on the string is the same. So :
$v = fL/2 = f'L'/2$.  
The amplitude of B is not important. Any amplitude will work, but the frequency is crucial.
How much lower than $f$ does $f'$ need to be? I think this cannot be answered exactly. If $L'$ is only slightly greater than $L$, the section BB' will be very steep. This will require the midpoint of the string to have a very large amplitude. A real string may not have enough elasticity to extend so much. To maintain the same amplitude the increase should be approximately proportional :
$f'/f=L/L'=AP/L$.  
If P were the midpoint of AB, then $L'=2L$ and $f'=\frac12 f$.
A: This additional answer assumes that the question is about shortening the length of a vibrating string during vibration.
If you are shortening the length of a string that is already vibrating in its fundamental mode, you are moving the resonant frequency to higher values corresponding to the changed length of the string.  This is a well-known phenomenon in violins, where during  shortening/lengthening the vibrating string length by continuously moving the pressure point on the finger board, a tone with increasing/decreasing pitch is produced. 
