Sound waves are always longitudinal waves in nature. This means that they travel by transferring energy from particle to particle. When multiple sound waves interfere with one another we see superposition occur. Superposition is where the net displacements of two waves are combined as they pass through each other. The resultant displacement is the vector sum of each waves’ displacements.
A stationary wave is formed from the superposition of two progressive waves that are travelling in opposite directions, but experience the same frequency, wavelength and amplitude. Energy is NOT transferred via stationary waves. Where waves meet in phase, see constructive interference occur so that antinodes are formed, which are zones of maximum amplitude. The opposite of these are nodes, which are zones of zero amplitude. This is when waves meet out of phase and destructive interference occurs.
Stationary waves can be observed physically by plucking strings on a string instrument. Plucking a string sends a wave of kinetic energy through the string from the plucking point. This wave then reflects (either at the nut or the bridge, depending on direction) back on itself and travels back along the string. Since the wave is reflecting on itself, the frequency, wavelength and amplitude are all the same. As such, superposition can be observed this way.
The lowest frequency at which a stationary wave forms is called the first harmonic, comprised of two nodes and one antinode. The difference between two adjacent nodes is always equal to half of one wavelength (for any harmonic). The first harmonic frequency can be doubled to find the second harmonic, etc for the nth harmonic.
As demonstrated by the above formula, shorter strings produce higher frequencies when plucked. This principle is used often when designing guitars. The optimum length and respective tensions of the strings can be determined by working backwards from the frequency that you’re trying to achieve. Specific frequencies create specific musical notes (for example, the E string on a bass guitar has a frequency of 41.2Hz.)
Similarly, the formula mathematically proves that tightening a string will increase the frequency of the resulting wave. Musicians tighten and loosen strings often in order to make sure the instrument is in tune. Over time, the strings experience repetitive strain as they are stretched out and tightened over and over. This repetitive strain is what causes failure in guitar strings. When a guitar string fails (breaks/snaps), it must be replaced.
Sudden snapping of the string can also cause strain on the neck of the guitar, as the neck works harder to support the sudden change in tension. It is best to replace the string as soon as possible to avoid any warping of the wood on the neck due to the severe change in tension.
Below is a video showing my own strings on my baritone ukulele, to demonstrate how the beginning of string failure may look. Please note that these are cheap, nylon-based strings, which tend to degrade faster than wire strings. Please also note that this instrument is not particularly well-looked after, as it is around 5 years old now and the tuning pegs are beginning to rust.