Editing Node (physics) (section)

== Boundary conditions ==
Where the nodes occur in relation to the boundary reflecting the waves depends on the end conditions or [[boundary conditions]].  Although there are many types of end conditions, the ends of resonators are usually one of two types that cause total reflection:

*<u>Fixed boundary</u>: Examples of this type of boundary are the attachment point of a [[guitar]] string, the closed end of an open pipe like an [[organ pipe]], or a [[woodwind]] pipe, the periphery of a [[drumhead]], a [[transmission line]] with the end [[short circuit]]ed, or the mirrors at the ends of a [[laser cavity]].  In this type, the amplitude of the wave is forced to zero at the boundary, so there is a node at the boundary, and the other nodes occur at multiples of half a wavelength from it:{{block indent | text = 0,&nbsp; λ/2,&nbsp; λ,&nbsp; 3λ/2,&nbsp; 2λ, ..., nλ/2}}
*<u>Free boundary</u>: Examples of this type are an open-ended organ or woodwind pipe, the ends of the vibrating resonator bars in a [[xylophone]], [[glockenspiel]] or [[tuning fork]], the ends of an [[Antenna (radio)|antenna]], or a transmission line with an open end.  In this type the [[derivative (calculus)|derivative]] (slope) of the wave's amplitude (in [[sound wave]]s the pressure, in electromagnetic waves, the [[Electric current|current]]) is forced to zero at the boundary.  So there is an amplitude maximum (antinode) at the boundary, the first node occurs a quarter wavelength from the end, and the other nodes are at half wavelength intervals from there: {{block indent | text = λ/4,&nbsp; 3λ/4,&nbsp; 5λ/4,&nbsp; 7λ/4, ..., (2n+1)λ/4}}