Destructive Interference of two waves

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Discussion Overview

The discussion revolves around the phenomenon of destructive interference of two sinusoidal pulses on a long string, focusing on the behavior of energy at the point of interference and subsequent motion of the pulses. Participants explore the implications of kinetic and potential energy during this interaction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions where the energy of the pulses goes at the point of destructive interference, noting that no crest or trough is formed, yet the pulses continue moving afterward.
  • Another participant asserts that at the point of interference, the energy is all kinetic energy.
  • A request for further clarification on the energy dynamics is made by a participant.
  • It is noted that while the string's position is at equilibrium during interference, it is still in motion, indicating the presence of kinetic energy.
  • One participant proposes a view of the meeting point as a fixed end, suggesting that the pulses reflect and invert, although they express uncertainty about the correctness of this reasoning.
  • Another participant challenges this reflection idea, arguing that reflection typically occurs due to changes in medium properties, which are absent in a homogeneous string.
  • The participant who suggested reflection acknowledges the inconsistency of this explanation but considers it a helpful way of thinking about the phenomenon.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of energy at the point of destructive interference, with no consensus reached on the explanation of the observed phenomena. The discussion remains unresolved regarding the nature of energy dynamics during interference.

Contextual Notes

Participants have not fully explored the assumptions regarding energy conservation and the nature of wave interactions in a homogeneous medium. The discussion includes speculative reasoning that has not been rigorously validated.

SDewan
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On a single long string, two sinusoidal pulses are started from either end. They have a destructive interference.
Both the pulses have kinetic as well as potential energy. Now the point at which they meet, there being a destructive interference, no crest or trough is formed. But right after that, they seem to have continued their initial respective motions.
My doubt: Where does their energy go at this point? How does it come back right after this point?
Solve my problem, please.
Thanks
SD
 
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SDewan said:
Where does their energy go at this point?
It is all KE at that point.
 
Please elucidate
 
"No crest or trough" means that the position of the string is all 0, the equilibrium position. But the string is not at rest, it is moving. Therefore it has KE.
 
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Intuition suggests that the energy is purely kinetic. But to explain this phenomena to myself I took the following view: Consider the point where the two pulses meet to be a fixed end. The pulse coming from the left gets reflected and also inverted, same with the other pulse. So while it appears to us as if the pulses have passed each other unscathed they actually are reflected and inverted.
I don't know how correct this is but it does provide some reasoning.
 
Last edited:
You can imagine that they reflect but this is inconsistent with general reflection behavior. Reflection happens when you have a change in the properties of the medium.
So why would you have reflection in the middle of a homogeneous string? There is no interface or discontinuity there.
 
nasu said:
You can imagine that they reflect but this is inconsistent with general reflection behavior. Reflection happens when you have a change in the properties of the medium.
So why would you have reflection in the middle of a homogeneous string? There is no interface or discontinuity there.
Yeah I get that.. That's why I said this wouldn't be a rigorous explanation, rather just a helpful way of thinking about it.
 

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