Standing waves (aka stationary waves)
Standing waves are an interesting physical phenomenon that show up in several places in nature. They’re a wave that oscillates “in place”.
One of the ways a standing wave can be created is by the interference of two waves travelling in opposite directions (like in the second image). By the superposition principle, the resulting wave (in black) is the addition of the both waves (red and blue).
This standing wave has points that remain fixed (called nodes, in red), where destructive interference always occurs, and points that oscillate the most (called antinodes), where constructive interference occurs.
Standing waves are behind the sound of virtually every acoustic musical instrument, whether it is a drum, a flute or a violin. The musician operates the instrument in a manner to generate a vibration, and the vibration is propagated and reflected throughout the instrument. The interference between all of the reflected waves generate standing waves, which is what ultimately produce the bulk of the sound we hear.
The waves shown here are one-dimensional, but this phenomenon occurs in two and three dimensions as well.
By studying how waves interfere and reflect, and how these generate standing waves, one can estimate the vibration and density inside a spherical body (such as the Sun or the Earth — read those links!) from measurements of oscillation on the surface, a very powerful tool for studying the inner workings of such structures.
In the third animation, for reference, we see the wave generated when opposing waves of different frequencies interfere. This is not a standing wave, as you can see, it does move to the right.