When Will Node and Antinode Energies Be Equal?

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Discussion Overview

The discussion revolves around the question of when the energy at a node in a wave is equal to the energy at an antinode, specifically in the context of wave mechanics. Participants explore concepts related to amplitude, potential energy, and kinetic energy within the framework of oscillatory motion.

Discussion Character

  • Homework-related, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant inquires about the specific time when node energy equals antinode energy during a wave's period T.
  • Another participant suggests that the inquiry appears to be homework-related and encourages the original poster to share their prior research or understanding.
  • A new user explains their understanding that nodes have zero amplitude while antinodes have maximum amplitude, and they reference the relationship between potential and kinetic energy but express difficulty in applying this to the original question.
  • A later reply emphasizes the need to consider both kinetic energy (KE) and potential energy (PE) at the antinode and prompts further exploration of energy at the node.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solution to the original question, and multiple viewpoints regarding the understanding of energy at nodes and antinodes are presented.

Contextual Notes

There are limitations in the discussion, such as the lack of specific mathematical relationships or assumptions that could clarify the energy dynamics at nodes and antinodes.

Who May Find This Useful

This discussion may be useful for students studying wave mechanics, particularly those grappling with concepts of energy distribution in oscillatory systems.

varunika
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at what time will the energy of a node be equal to energy of an antinode when the time period is T?
 
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Hi
Looks like homework (which should be posted elsewhere - see the top of the list of topics). What do you think about this and what research have you done already? PF makes a point of not just giving answers without the student having shown they have tried a bit.
 
sorry... actually m a new user on this website...unaware of the rules..
what i know is...
that node has zero amplitude..n antinode has maximum amplitude. and that the maximum potential energy= 1/2*ρ*ω2A2.
which also equals the kinetic energy..
but i am unable to relate the above information in order to solve the given query.
please guide me if i m wrong anywhere.
 
Last edited:
Afair, you need to consider the sum of KE and PE at the Antinode. What will the energy be at a node? This link gives a good treatment for strings. I think the answer to your question in in there.
 

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