Solving for Constant in T=k/L Inverse Proportionality

In summary, the tension of a string is inversely proportional to its length and can be represented by T=k/L, where T is the tension, k is the constant, and L is the length. Upon quantization of the string, the characteristic string length L is related to the tension T by L=1/(sqrt{pi*T}). This relationship is responsible for the tension along the string and can vary depending on the energy scale. The length is indeed a constant and T can be found by solving for k in the equation T=k/L.
  • #1
Matrixman13
32
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I know that the tension of a string is Inversely proportional to the length. obviously this is shown as T=k/L, where t is the tension; k is the constant; and L is the length. My question is; What is the constant? I would also appreciate anything else loosely related to the topic. Thank you.
 
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  • #2
Upon quantization of the string, the characteristic string length L is related to the string "tension" T (the characteristic energy scale) by L=1/(sqrt{pi*T}).
 
  • #3
What is responsible for the tension along a string? Is the tension you equated above the average tension along the string? Could tension change along the string?
 
  • #4
Javier said:
Upon quantization of the string, the characteristic string length L is related to the string "tension" T (the characteristic energy scale) by L=1/(sqrt{pi*T}).

Isn't the length a constant? How do you find T?
 

What is the equation for inverse proportionality?

The equation for inverse proportionality is T = k/L, where T is the dependent variable, k is the constant of proportionality, and L is the independent variable.

What does the constant of proportionality represent?

The constant of proportionality, k, represents the relationship between the dependent and independent variables in an inverse proportion. It is a fixed value that remains the same regardless of the values of T and L.

How do you solve for the constant of proportionality?

To solve for the constant of proportionality, k, you need to have at least two sets of data points for the dependent and independent variables. Then, you can plug in the values into the equation T = k/L and solve for k.

Can the equation for inverse proportionality be used for any type of relationship?

No, the equation for inverse proportionality can only be used for relationships where the two variables are inversely proportional to each other. This means that as one variable increases, the other decreases at a constant rate.

What happens if the value of the constant of proportionality is negative?

If the value of the constant of proportionality is negative, it means that the two variables are inversely proportional, but the relationship between them is negative. This means that as one variable increases, the other decreases, but the values will be in opposite directions.

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