What is the length of a vibrating metal wire at its third harmonic frequency?

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Homework Help Overview

The problem involves a vibrating metal wire at its third harmonic frequency, with a specific point along the wire where the amplitude is one quarter of the maximum amplitude. The task is to determine the length of the wire based on this information.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the interpretation of the distance of 0.32 m from one end, particularly whether it refers to a node or an antinode. There is also uncertainty about whether the wire is fixed at one or both ends, which affects the understanding of the harmonic setup.

Discussion Status

Participants are actively exploring the implications of the problem's setup, with some providing hints about the relationship between wavelength and the length of the string in the context of the third harmonic. There is a focus on clarifying assumptions regarding the boundary conditions of the wire.

Contextual Notes

There is ambiguity regarding the fixed ends of the wire and the definition of the points along the wire in relation to nodes and antinodes. The problem includes a hint about the wavelength and amplitude that may influence the interpretation of the setup.

goonking
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Homework Statement


A metal wire is vibrating at its third-harmonic frequency. 0.32 m from one end, the amplitude is equal to one quarter the maximum amplitude. Find the length of the wire.

Homework Equations

The Attempt at a Solution


I don't quite understand the question, it says 0.32m from one end, is that from the start to the first node?

the amplitude going to be 1/4 its maximum where sin(x) = 0.25, correct?
 
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goonking said:
A metal wire is vibrating at its third-harmonic frequency. 0.32 m from one end, the amplitude is equal to one quarter the maximum amplitude. Find the length of the wire.
It is not clear to me whether the wire is fixed at either or both ends. I'd guess it's fixed at both. If so, the 'start' is a node, and .32m is the distance from there to the given point.
goonking said:
the amplitude going to be 1/4 its maximum where sin(x) = 0.25, correct?
It depends what you mean by x.
 
haruspex said:
It is not clear to me whether the wire is fixed at either or both ends. I'd guess it's fixed at both. If so, the 'start' is a node, and .32m is the distance from there to the given point.

It depends what you mean by x.
if it helps, the hint the question has is : "The third harmonic will have a wavelength equal to 2/3 of the length of the string. Also, *note to self* the max-amplitude of this wave is (2A) not (A)."
 
goonking said:
if it helps, the hint the question has is : "The third harmonic will have a wavelength equal to 2/3 of the length of the string. Also, *note to self* the max-amplitude of this wave is (2A) not (A)."
So what does that tell you about whether one or both ends of the string are nodes?
 

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