Webpage title: Calculating Distance Between Nodes in a Standing Wave on a String

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The discussion centers on calculating the distance between adjacent nodes in a standing wave formed by the superposition of two traveling waves, represented by the equations y1=Asin(ωt−kx) and y2=Asin(ωt+kx). The initial confusion arises from understanding how the distance between nodes relates to the wave equations. It is clarified that the distance between two nodes is derived from the relationship 2π/k, leading to the conclusion that the distance between adjacent nodes is π/k. The phase shift of the waves is also noted as a key factor in determining this distance. The final answer emphasizes the connection between wave properties and their spatial characteristics.
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The question is: "Two traveling waves are superposed on the same string. Waves are y1=Asin (ωt−kx) and y2=Asin(ωt+kx).The distance between adjacent nodes of the resulting standing wave is: "

This is the question I have tried to solve.
I know that the distance between two nodes is 2pii. Then I do not know how to proceed.

The answer is pii/k,
but I do not know how it is obtained.

Please, do not hesitate to reply if you know why the answer is pii/k.

Thank you in advance!
 
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-kx and +kx is the phase shift of the two waves. How far apart are the two waves then? How can you relate this to the period and the distance, x?
 
Thank you, you solved this question as 2pii=2kx => Distance(x)=pii/k.
 

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