Editing Node (physics) (section)

== Explanation ==
[[File:Node.svg|thumb|Pattern of two waves' interference (from up to down). The point represents the node.]]
[[Standing wave]]s result when two [[sinusoidal wave]] trains of the same [[frequency]] are moving in opposite directions in the same space and [[Interference (wave propagation)|interfere]] with each other.<ref>{{cite book
  | last = Feynman
  | first = Richard P.
  |author2=Robert Leighton |author3=Matthew Sands
   | title = [[The Feynman Lectures on Physics|The Feynman Lectures on Physics, Vol.1]]
  | publisher = Addison-Wesley
  | year = 1963
  | location = USA
  | pages = ch.49
  | url = 
  | doi = 
  | id = 
  | isbn = 0-201-02011-4}}</ref>  They occur when waves are reflected at a boundary, such as [[sound wave]]s reflected from a wall or [[electromagnetic wave]]s reflected from the end of a [[transmission line]], and particularly when waves are confined in a [[resonator]] at [[resonance]], bouncing back and forth between two boundaries, such as in an [[organ pipe]] or [[guitar string]].

In a standing wave the '''nodes''' are a series of locations at equally spaced intervals where the wave [[amplitude]] (motion) is zero (see animation above).  At these points the two waves add with opposite [[phase (waves)|phase]] and cancel each other out.  They occur at intervals of half a [[wavelength]] (λ/2).  Midway between each pair of nodes are locations where the amplitude is maximum.  These are called the '''antinodes'''.  At these points the two waves add with the same phase and reinforce each other.

In cases where the two opposite wave trains are not the same amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero but merely a minimum.  This occurs when the reflection at the boundary is imperfect.  This is indicated by a finite [[standing wave ratio]] (SWR), the ratio of the amplitude of the wave at the antinode to the amplitude at the node.

In [[resonance]] of a [[two dimensional]] surface or membrane, such as a [[drumhead]] or vibrating metal plate, the nodes become nodal lines, lines on the surface where the surface is motionless, dividing the surface into separate regions vibrating with opposite phase.  These can be made visible by sprinkling sand on the surface, and the intricate patterns of lines resulting are called [[Chladni figure]]s.

In [[transmission line]]s a [[voltage]] node is a [[Electric current|current]] antinode, and a voltage antinode is a current node.

Nodes are the points of zero displacement, not the points where two constituent waves intersect.