For a standing wave on a string the wavelength must equal:Select one:a.the distance between adjacent nodes.b.the distance between supports.c.twice the distance between adjacent nodes.d.the distance between adjacent antinodes.
Question
For a standing wave on a string the wavelength must equal:Select one:a.the distance between adjacent nodes.b.the distance between supports.c.twice the distance between adjacent nodes.d.the distance between adjacent antinodes.
Solution
The correct answer is c. twice the distance between adjacent nodes.
Here's why:
A standing wave on a string is created by the superposition of two waves traveling in opposite directions. This creates points of constructive interference (antinodes) and destructive interference (nodes).
The distance between two adjacent nodes or two adjacent antinodes is half of a wavelength. This is because a full wave cycle includes a crest and a trough, and the distance between a node and an antinode represents only half of this cycle (either a crest or a trough, but not both).
Therefore, to get the full wavelength, you need to consider the distance between two nodes or two antinodes twice, which is the same as the distance between every second node or antinode. Hence, the wavelength must equal twice the distance between adjacent nodes.
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