The animated image below is an simple simulation of sound waves traveling in air. For purposes of debugging the speed of sound in air as been arbitrarily set to 1 foot per second.
There are two sources of sound in the diagram. The primary one, called "the source" is 40 feet left of the origin on the X axis. It is emitting a constant power of 0.02 watts at 0.2 cycles per second.
The second source of sound is called "the emitter". It is located 3 feet left and 4 feet above the origin. It is tuned to the same frequency as the source with power level and phase set so that it will exactly cancel out the source at the origin.
The data values on the diagram are the absolute value of the pressure wave amplitude, converted to decibels and then plotted as shades of grey. Each frame of the animation is scaled from pure white at the maximum value down to black at the minimum value. There are 20 frames in the animation with one eighth second (in simulation time) between them.
There are two red circles in the diagram. One is centered on the source with a radius of 40 feet. The other is centered on the emitter with a radius of 5 feet. This naturally has the circles intersect at the origin which is the main point of interest. However, as you can see in the animation the other point where the circles intersect also always has zero amplitude.
The individual frames where generated as PNG files by a custom Perl program using Image::Magick. The animation GIF file was created in Adobe ImageReady.