Wavelength (1967) is an experimental film by filmmaker Michael Snow.

This 45 minute long, 16 mm color film is centered around a single shot in a room; one long zoom narrowing the frame from the entire room to a photograph of the ocean on a far wall.

In the duration, a few events occur. People come into the room and turn on and off a radio (Strawberry Fields Forever by The Beatles is playing). Filmic techniques such as filtering and inverting of the image are used. Towards the end, a man walks in and apparantly dies. Later, a woman comes in and finds the dead man and calls someone on the phone to share the news.

Meanwhile, the soundtrack (in addition to the diegetic sounds) consists of a sine wave slowly rising from a low frequency to a high frequency (or long wavelength to short wavelength). This sound was apparantly made with a cheap synthesizer, because throughout the film, one can hear the difference tones created with the 60 Hz line frequency. These difference tones, though add an interesting dimension to the soundtrack.

Aesthetically, Wavelength is closely related to the contemporaneous formalist/minimalist music of Steve Reich and James Tenney. Its strict formalism is somewhat violated by the seemingly intuitive or arbitrary hints of narrative and visual effects, but in the end, the all-encompassing structure sets aside minor inconsistencies and stands on its own as a classic.

For a periodic wave, the wavelength is the distance after which the wave repeats its shape1. The wavelength is usually denoted with the Greek letter λ and has dimensions of length. For a perfect sinusoidal wave, the wavelength can be measured as the distance between one crest and the next or one trough and the next. If a wave has a long wavelength, it changes very slowly over distances. If the wavelength is small then it changes very rapidly over distances. The wavelength describes the behavior of a wave in space in the same way that the period describes the behavior in time. If a traveling wave varies in time with a period T, then the speed of the wave will be λ/T.

Mathematically, a sinusoidal wave takes on values according to the expression

A cos(2πx/λ+φ)

at a position x. This expresses the fact that the value for x = 0 will be the same as for x = λ, since that would just add 2π to the argument of cosine, which does not change the value. It is true that the value is the same for any two points separated by a distance λ. Often when dealing with the mathematics of waves it is more convenient to describe the behavior in terms of wavenumber rather than wavelength. In general, a wave that is not perfectly sinusoidal is made up of a superposition (the addition of) many sinusoidal waves of different wavelengths.

As it characterizes a wave, the wavelength will determine how many other wave phenomina exhibit themselves, including: interference, diffraction, dispersion, and the available resolving power.

Wavelength is one of the properties of a wave that is often easiest to measure. If a wave is standing still or not moving very quickly, then one may be able to measure the wavelength directly. For example, if you setup a standing wave on a string, then you can actually use a ruler to measure the wavelength. Often we measure the wavelength indirectly using interference patterns, especially when the wavelength is very small.

A sort of wavelength that scientists are often concerned with measuring is the wavelength of light, which is an electromagnetic wave. The wavelength of visible light is quite small, ranging from about 400-700 nm, but it can be measured through diffraction and interference. By measuring the wavelength of light we can determine the energy of the process that emitted that light. This allows us to determine the temperature of distant objects and the internal structure of atoms and molecules, in a process known as spectroscopy. The wavelength is important in most of the processes of physical optics.

In quantum mechanics, all particles travel as waves. One of the early steps in quantum mechanics was the discovery of de Broglie's relation, which relates the wavelength of a particle's wavefunction to its momentum.


1 One may assign a wavelength to any periodic wave; however, if it is not perfectly sinusoidal, then one may actually assign a number of different wavelength components to it through fourier analysis. The wavelength of periodic repetition would be the stongest component.

The concept of wavelength is something I take for granted so much I wasn't entirely sure what to put. Suggestions for improvements are more than welcome.

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