Can you eliminate sound vibration (when either it is audible sound, ultrasound or infrasound) by creating a destructive interference, but when both sources are in opposite sides?
Say, you have one audio speaker playing in one corner of the room and another speaker in an opposite corner?
Points of destructive interference will be highly localized, especially in the case of ultrasonic sound.
In order for near complete destructive interference to occur: everything has to line up just right. The two propagating sounds must be perfectly out of phase, and they must be of the same amplitude (the same loudness).
Ultrasonic sound has the following property: as it propagates it loses amplitude rapidly, it loses energy. Ultrasonic sound loses amplitude more rapidly than audible sound does.
So the only way to have a decent chance of obtaining desctructive interference that is not highly local is to have the two sounds co-propagating, rather than having the sound and the counter-sound coming from opposite direction.
For comparison the opposite problem: how to have speakers assist each other.
When setting up a sound system for a stadium concert there are the speakes right next to the stage, and there are are additional speakers for audience seated a long distance away from the stage.
The speaker system for the long-distance-away audience are called 'delay towers'.
Sound take time to travel. So the sound that is blasted out by the delay towers is delayed a bit relative to the next-to-the-stage speakers, so that as the sound from the next-to-the-stage speakers arrives the sound that is blasted out the delay towers lines up with it.
So:
Having multiple sources line up in such a way that the resulting sound is constructive is already very tricky.
Getting to near complete destructive interference for a usefully large amount of space would be very, very tricky.
Later edit, in response to a request in the comment section:
In general: the longer the wavelength of sound, the slower the process of losing amplitude as the sound propagates. Conversely, the shorter the wavelength, the more rapid the process of dissipation of energy.
Example: when a lightning strike occurs close by the sound is like sharp explosion; a large proportion of the sound energy is high pitched. When you hear thunder rolling in from miles away its a rumbling sound. The low frequency end of the spectrum has made it all the way, the sound energy of the higher frequencies has dissipated.
Propagating sound is a propagating longitudinal oscillation of compression and rarefication. When air is compressed there is a corresponding rise in the temperature of the air.
Compare the case of compressing air in a piston. As air is being compressed the temperature of the air rises. If you right away allow the air to expand again then most of that energy is recovered. Still, some of the heat will transfer to the wall of the piston. The energy that has leaked away is no longer available for transformation back to mechanical motion.
In the case of propagating sound:
Sound propagates far because most of the energy remains sound energy. However, some of the heat energy does leak, it moves down the temperature gradient. So, instead of all the energy remaining in the form of sound energy some of it becomes uniform heat. The higher the frequency of the sound, the larger the rate of dissipation.
Yes, it is possible to eliminate sound in one (or some) points where you'll have a node of the wave. It will not be very efficient and probably you will have some background sound coming from reflections of the waves with the walls and objects in the room.
Check this video, it is in Spanish but at around 5:40 they make the experiment: Sound interferences
There will be destructive interference midway between the speakers if both speakers are playing the same pure notes (same frequencies) at the same loudness (same amplitude). Since the path lengths from the speakers to the midway point are equal the waves will arrive at the midway point in antiphase when the speakers are in phase with each other. This is because sound is a longitudinal wave and the waves from the two speakers are travelling to P in opposite directions. There won't, though, be silence at the midway point even if the sounds have the same loudness (same amplitude), because waves will reach this point by paths involving reflections as well as straight from the speakers, and it would be unlikely that the sound travelling by these 'extra' routes will cancel.
There are other points, P, in the room where destructive interference will occur, but only for certain frequencies of sound. If S$_1$ and S$_2$ are the positions of the speakers, and P is on the 'diagonal' line $\text S_1\text S_2$ then for in phase speakers $$|\text S_2 \text P-\text S_1 \text P|=n\lambda $$
Here, $\lambda$ is the wavelength of the sound, given by $\lambda=\frac vf$ in which $f$ is the frequency and $v$ is the speed of sound in air. $n=1, 2, 3 ...$. We've already dealt with the case of $n=0$.
Silence at P, even if this condition is met, is unlikely, as the amplitudes are unlikely to be equal, and there will be paths other than the direct ones.
For points, P, not on the 'diagonal' line $\text S_1\text S_2$, full destructive interference won't take place as the oscillating displacements will be in the alignments $\text S_2 \text P$ and $\text S_1 \text P$ and therefore can't be in opposite directions.
