Wave Equation

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered. From the ratio, using the value of θ, and...

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete. However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...

Source: Arianna Brown, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA Standing waves, or stationary waves, are waves that appear not to propagate and are produced by the interference of two waves traveling in opposite directions with the same frequency and amplitude. These waves appear to vibrate up and down with no linear movement and are most easily identified in vibrating finite media like a plucked guitar string,...

Source: Arianna Brown, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA Waves are disturbances that propagate through a material medium or empty space. Light waves can travel through a vacuum and some forms of matter, and are transverse in nature, which means that the oscillations are perpendicular to the direction of propagation. However, sound waves are pressure waves that travel through an elastic medium like air,...

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms and was able to demonstrate that white light consists of the individual colors of the rainbow combined together. Newton explained his optics findings in terms of a "corpuscular" view of light, in which light was composed of streams of extremely tiny particles traveling at high speeds according to Newton's laws of motion. Others in the...