Note on Standing Wave Nodes

Many of you working on the standing wave lab confused the condition for an antinode and odd half periods with the conditions for a node. Note that there is usually no difference in effect between odd and even WHOLE periods. Odd HALF periods are needed for ANTInodes if a phase shift occurs on reflection. [SEE the Notes published on Feb 12 on this blog]

For a point on a string or similar medium to be a standing wave node, waves arriving from the left and from the right must be out of phase at all times. A fixed end produces a half cycle wave shift in a reflected wave. If a wave passes through a node say going left travels to a fixed end and gets reflected by the fixed end and then travels back that is to the right ( now shifted by half a cycle) to that node, it will arrive at the node out of phase with waves traveling to the left if it takes ANY INTEGER (even or odd) number of periods to make the round trip from node to end and back to node.

This is consistent with the fact that there are an integer number of loops between any node and any fixed end and each loop is half a wavelength. Therefore the round trip will include twice the number of loops as the one way trip from node to the end and therefore an even number of loops. The number of loops is equal to half as many wavelengths but half of an even number is always an integer. Therefore the round trip is an integer number of wavelengths and takes an integer number of periods. [ Remember wavelength = speed x period so a distance of N wavelengths takes a time of N periods].