Resonance in String: Understanding Wave Interference According to Book

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Discussion Overview

The discussion revolves around the concept of wave interference in a string, specifically addressing how a wave crest generated by a vibrating fork interacts with subsequent crests and the implications of this interaction on the understanding of resonance. The scope includes theoretical considerations and conceptual clarifications regarding wave behavior in a driven and damped system.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the assumption that a wave crest travels a distance of 2L without interference from subsequent crests generated by the fork.
  • Another participant suggests that the author’s presentation is simplified and emphasizes that all parts of the incoming wave interfere with all parts of the reflected wave.
  • A participant raises a concern about the validity of the formula ##f=\frac{n}{2l}\sqrt{\frac{T}{\mu}}## in the context of the discussion.
  • One participant responds by indicating that the context of the formula is crucial and that its applicability may depend on specific conditions.

Areas of Agreement / Disagreement

Participants express differing views regarding the assumptions made in the author's explanation, indicating that there is no consensus on the interpretation of wave interference in this scenario.

Contextual Notes

There are limitations in the discussion regarding the mathematical treatment of the wave behavior, as some participants note a lack of necessary mathematical tools to fully analyze the driven and damped system described.

AdityaDev
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according to book "...Let us look at a particular wave crest generated at the left end of the string by a fork. It travels to the right end of the string, is reflected back, and is reflected again at the fork.Now it interferes with the next wave..."
doubt: the fork keeps vibrating and keeps producing waves. so just after it is reflected from the right end, it will interfere with the next crest right? why didthe author assume the first crest traveled 2L distance without interference? wouldn't it interfere withe next frest just after it travels a distance L?
 
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The author is presenting a simplified picture. You should realize that all parts of the "incoming wave" interfere with all parts of the "reflected wave" to produce the wave you actually see.

The setup described is both driven and damped - but you don't have the maths for that yet.
 
Simon Bridge said:
The author is presenting a simplified picture. You should realize that all parts of the "incoming wave" interfere with all parts of the "reflected wave" to produce the wave you actually see.

The setup described is both driven and damped - but you don't have the maths for that yet.
So the formula ##f=\frac{n}{2l}\sqrt{\frac{T}{\mu}}## is wrong?
 
Wrong for what purpose?
Context is everything.
 

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