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:
- Fixed boundary: 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 circuited, 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:
-
- 0, λ/2, λ, 3λ/2, 2λ, ...
- Free boundary: 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, or a transmission line with an open end. In this type the derivative (slope) of the wave's amplitude (in sound waves the pressure, in electromagnetic waves the 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:
-
- λ/4, 3λ/4, 5λ/4, 7λ/4, ...
Read more about this topic: Node (physics)
Famous quotes containing the words boundary conditions, boundary and/or conditions:
“The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.”
—Willard Van Orman Quine (b. 1908)
“If you meet a sectary, or a hostile partisan, never recognize the dividing lines; but meet on what common ground remains,—if only that the sun shines, and the rain rains for both; the area will widen very fast, and ere you know it the boundary mountains, on which the eye had fastened, have melted into air.”
—Ralph Waldo Emerson (1803–1882)
“The circuited city of the future will not be the huge hunk of concentrated real estate created by the railway. It will take on a totally new meaning under conditions of very rapid movement. It will be an information megalopolis.”
—Marshall McLuhan (1911–1980)