Curious about Linear Density (μ) of a string

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Homework Help Overview

The discussion revolves around the concept of linear density (μ) in the context of a string used in musical instruments, specifically relating to the equation v = sqrt(T/μ). Participants are exploring the appropriate value for length (L) when calculating linear density, particularly when a string is stretched.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether to use the original length of the string or the stretched length when calculating linear density. There is a specific focus on the implications of stretching the string and how it affects the value of L.

Discussion Status

The discussion includes differing opinions on which length to use for calculations. Some participants suggest using the stretched length, while others express uncertainty and seek clarification on the implications of their choice.

Contextual Notes

Participants note that in typical musical instruments, significant stretching of the string is not common, and linear density is generally dependent on the material and diameter of the wire. There is also mention of a specific scenario that requires a decision between unstretched and stretched lengths.

erinec
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(Sorry I cannot follow the question format because this question is related to a problem, but is not the problem itself.)

I am talking about the linear density μ that appears in this equation:
v = sqrt(T/μ)

.. used usually for musical instruments, where μ = m/L

Now, I am wondering which value of L we use.

Say that you have a string that is normally .1 kg and .10 meters long.
Now let's say that u stretch the string to .12 meters to make some musical instrument.

For L value, do we plug in .12 meters or .10 meters?

Thanks!
 
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Usually in the musical instruments that mush stretching is not allowed. mu is the linear density of the wire. For a given length of wire ( which is usual in all the string instruments) linear density depends on the diameter and the material of the wire.
 
But I specifically came across a question that required me to make a choice between using an unstretched length vs. a stretched length and I wasn't sure what to do.Let's hypothetically assume that someone stretched a .1 m wire to .12 m to create some musical instrument.
Which value of L would u use?
 
Obviously 0.12 m.
 

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