Calculate number of nodes in stationary waves

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Homework Help Overview

The discussion revolves around calculating the number of nodes in stationary waves for a vibrating cord under different mass conditions. The original poster presents a scenario involving two different masses and their corresponding frequencies, seeking to determine the number of nodes in each case.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the harmonic number and the number of nodes, with some suggesting a correction to the original poster's interpretation of the number of additional nodes. There is also a question regarding the definition of nodes in relation to the fundamental frequency of the string.

Discussion Status

The conversation includes various interpretations of the problem, with some participants offering insights into the harmonic numbers and their corresponding nodes. There is a mix of agreement and differing opinions on the definitions and calculations involved, indicating an ongoing exploration of the topic.

Contextual Notes

Participants are considering the implications of different mass values on the frequency and node count, as well as the definitions of nodes in the context of stationary waves. The original poster's approach to the problem is questioned, and there is a lack of consensus on certain definitions.

markus92
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Homework Statement



Hi guys I have this problem that I can't solve..

Suppose to have this situation:

12345.jpg


when M=16kg the cord vibrates in one of its normal ways of oscillation.
when M=6.25 we have the same frequency but 3 more nodes.

How many are the nodes of the stationary wave in the first and in the second case?Knowing that for the n harmonic the frequency is

\frac{n}{2L}\sqrt{\frac{T}{u}}

3more node → n harmonic first case +2 so

\frac{n1}{2L}\sqrt{\frac{T1}{u}}=\frac{n2}{2L}\sqrt{\frac{T2}{u}}

but it's wrong.

How can I solve this?

Thanks in advance.
 
Last edited:
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I think i would be n+3 not n+2 for three more nodes
 
yes I think you're right

edit.

solved
 
Last edited:
I worked the problem and I am curious what the answer is?
 
Let me ask for a definition. If the string is vibrating at its lowest frequency, do you consider the endpoints f the string where it attaches to the wall and pully nodes or do the nodes only exist BETWEEN the end points? Put another way does the fundamental frequency have 0 or 2 nodes?
 
I consider the fundamental have 2 nodes like this schema

250px-Harmonic_partials_on_strings.svg.png
 

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