o any reference point in the medium. Let u be the direction of the oscillations (another unit-length vector perpendicular to d). The displacement of a particle at any point p of the medium and any time t (seconds) will be where A is the wave's amplitude or strength, T is its period, v is the speed of propagation, and φ is its phase at o. All these parameters are real numbers. The symbol "•" denotes the inner product of two vectors. By this equation, the wave travels in the direction d and the oscillations occur back and forth along the direction u. The wave is said to be linearly polarized in the direction u. An observer that looks at a fixed point p will see the particle there move in a simple harmonic (sinusoidal) motion with period T seconds, with maximum particle displacement A in each sense; that is, with a frequency of f = 1/T full oscillation cycles every second. A snapshot of all particles at a fixed time t will show the same displacement for all particles on each plane perpendicular to d, with the displacements in successive planes forming a sinusoidal pattern, with each full cycle extending along d by the wavelength λ = v T = v/f. The whole pattern moves in the direction d with speed V. The same equation describes a plane linearly polarized sinusoidal light wave, except that the "displacement" S(p, t) is the electric field at point p and time t. (The magnetic field will be described by the same equation, but with a "displacement" direction that is perpendicular to both d and u, and a different amplitude.) Superposition principle In a homogeneous linear medium, complex oscillations (vibrations in a material or light flows) can be described as the superposition of many simple sinusoidal waves, either transverse or longitudinal. The vibrations of a violin string, for example, can be analyzed as the sum of many transverse waves of different frequencies, that displace the string either up or down or left to right. The ripples in a pond can be analyzed as a combination of transverse and longitudinal waves (gravity waves) that propagate together. Circular polarization If the medium is linear and allows multiple independent displacement directions for the same travel direction d, we can choose two mutually perpendicular directions of polarization, and express any wave linearly polarized in any other direction as