Relationship Between String Tension and Stretch

[BraedenP]

Homework Statement

Will stretch in a string have an effect on the graph of wavelength vs. tension, relative to the same graph using a string without stretch?

Homework Equations

N/A

The Attempt at a Solution

No calculations are required, so I'm assuming that the slope of that graph in the string that stretches will be lower than the slope of the graph based on the string that doesn't stretch. This is all the information I really need to get the rest of the answer to the question.

tl;dr: Does stretch in a string affect its tension in a negative or positive way?

Thanks!
Braeden

 

[rock.freak667]

Well tension in a spring can be modeled as a spring such that T=kx. But what exactly is the 'wavelength' that you are measuring?

 

[BraedenP]

Well tension in a spring can be modeled as a spring such that T=kx. But what exactly is the 'wavelength' that you are measuring?

That would probably be some useful information, wouldn't it? :P

We're attaching the string to a speaker and vibrating it at 60Hz. Then we're hanging a mass on the string over the edge of a table, and moving the speaker until we get a tension that creates even oscillations.

We then calculate the wavelength from measuring the string directly.

 

[rock.freak667]

This page might help you as well, it is on vibrating strings.

 

[rwisz]

I would approach this question by first understanding the relationship between string tension and stretch. When a string is stretched, it experiences an increase in tension due to the forces acting on it. This increase in tension is directly proportional to the amount of stretch in the string. Therefore, it can be said that the tension in a string is affected by the amount of stretch it experiences.

In terms of the graph of wavelength vs. tension, using a string with stretch will result in a lower slope compared to using a string without stretch. This is because the tension in the string with stretch will be greater for a given amount of stretch, resulting in a smaller change in wavelength for a given change in tension.

In summary, the relationship between string tension and stretch is a positive one. As the stretch increases, so does the tension in the string. This will result in a lower slope on the graph of wavelength vs. tension for a string with stretch compared to one without stretch. Therefore, it is important to consider the amount of stretch in a string when studying its tension and its effect on other variables.