Notes on Standing Waves

Do NOT confuse crests or troughs with nodes. Maximum crests and minimum troughs have the same amplitude, just different signs, and occur at antinodes. Nodes ( not antinodes) are where there is no change because there is always destructive interference. A wave crest passing through a point going to the left will come back reflected from a fixed end as a trough going to the right. If the point is to be an antinode this reflected wave must return to the point an odd number of half periods later so that another, unreflected (i.e.”original”) wave going to the left will also be a trough, so that you will have constructive interference between the two waves.

For a place to be a node other than at the end of the string, it must have continuous destructive interference. That means that the wave reflected with a phase change must arrive an integer number of periods after the original wave passes through, or 2 x distance from node to end = integer number of wavelengths. The distance between a node and any antinode is always an odd number of quarter wavelengths. The distance between any two nodes is an integer number of half wavelengths. The distance between two antinodes is an integer number of half wavelengths. Draw a sketch and you will see all this.