Standing Waves

Video 1 is a good illustration of how standing waves behave, in air and otherwise. Standing waves are easy to produce on this string, because it is a closed system - the string is tied at both ends, so the wave itself bounces straight back along the string because it has nowhere else to go, so the energy cannot escape (much). Additionally, we can see that the standing wave that is produced is analogous as any sine wave we might draw when looking at an analogue electrical signal. The nodes and anti-nodes map exactly to the pattern of compressions and rarefactions we would get with a standing wave in air.

Bear in mind while watching Video 1 that wavelength (λ) is the measurement of the distance between the start and the end of a full wave cycle - that is, from one 'peak' point to the next 'peak,' not to the next 'trough', which is the maximum negative amplitude the wave reaches, but is the halfway point of a full cycle before returning to maximum positive amplitude at the peak. This is illustrated in Fig. 1 for clarity.

The same applies with acoustic instruments, and standing wave theory is quite important when designing instruments to get the desired pitch. The length of a flute, for example, is modified when the flautist covers the different holes. This produces a different note because the standing wave in the instrument is interrupted by this potential 'escape route' for the air pressure, thereby affecting the frequency at which the air in the flute vibrates because the wavelength has changed.

Acoustical Properties of a Standing Wave
Through the same process by which the standing waves are generated on the string in Video 1, every single acoustic sound which is produced - including a music instrument, human speech, crashes, bangs, anything - is simply made up of a large number of sine waves layered on top of each other because of standing wave theory. To explain this, it is important to understand some of the terminology here: The human voice is rich in harmonics because of the complexity of our voicebox, and the way that sound resonantes through our entire bodies when we speak. Everything that is vibrated produces a sound, so really it is very difficult to find a 'pure tone' or single, isolated sine wave in nature. Likewise when plucking or bowing a string on a violin, the waves bouncing around on the closed system of the string produce their own harmonics as well. All of these standing waves are present simultaneously in an acoustically produced musical note. Observe how the waves reflect back and forth over one another in Video 3.
 * Node - A point in a standing wave where destructive interference has created a point where no overall movement is occurring.
 * Anti-node - A point in a standing wave where constructive interference has created a point where the maxmium amount of possible movement (twice the amplitude of the original source wave) is occurring.
 * Fundamental frequency - the fundamental frequency of a wave is the loudest frequency at which the wave vibrates. For example, if you pluck an E string on a guitar, the fundamental would be the lowest, loudest E that can be heard. It is virtually impossible for the human ear to pick out other harmonics created by plucking a string, but they are crucial in making up the richness of the overall sound and occur everywhere naturally.
 * Harmonics - Harmonics are the name we give to the higher-frequency standing waves generated whenever a sound is produced. In acoustic instruments, this factor is deliberately used to create particular resonances and generate a predetermined pitch or note for the instrument. Each one of those notes will produce a number of harmonics at mathematically related higher frequencies (as explained in video 2), and these are known as its harmonics.
 * Constructive and Destructive Interference - Interference is just what happens when two waves collide with each other - they have an effect on each other. In a closed system like the electrically driven string in Video 1, or the violin string in Video 3, these waves can consistently reflect back onto each other at particular frequencies. When they meet, if their peaks and troughs overlap then they constructively interfere with each other, creating an anti-node where the high amplitude of the waves sum with each other to create a larger peak. Likewise, a node is created when two points of unity or zero amplitude overlap and create no movement, because zero amplitude plus zero amplitude = zero movement.



Further Illustrations and Applications of Standing Waves
There are a number of interesting applications for standing waves, especially because they are so useful for visualising sound waves in air:







Standing Waves Summary

 * Standing waves are created when sound pressure waves reflect back upon themselves, summing together and producing static points (nodes) and points with a lot of movement (anti-nodes)
 * Standing waves are present in every acoustically produced sound, and give way to the phenomenon of harmonics
 * Standing waves are consciously manipulated in the construction of acoustic instruments and have other, more visual and aesthetic applications as seen above