Why Does My Calculation of Wire Length Differ from the Textbook's Answer?

In summary, the length of wire is a measurement that refers to the distance between two points on a wire, typically measured in meters. It can be measured using various tools and can be affected by factors such as temperature, tension, and material composition. The length of wire is important in industries such as electrical engineering, telecommunications, and construction. It can be altered by stretching or compressing, but this may impact its properties and performance.
  • #1
kasse
384
1
[SOLVED] length of wire

Homework Statement



A wire of mass 1.1 g is under a tension of 100 N. If its third overtone is at a frequency of 750 Hz, calculate the length of the wire.

The Attempt at a Solution



v = sqrt(FL/m) = 301.5*sqrt(L)

fn = n*v/(2*L) --> L = n*v/(2*fn) --> L = 0.36 m

The book says 0.65 m. Am I wrong?
 
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  • #2
The third "overtone" is the fourth "harmonic."

Other than that, you did everything right. (well, your final formula is incorrectly written, but you solved correctly for n=3.)
 
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  • #3




Based on your calculations, it seems that the length of the wire should be 0.36 m. However, the book states that it is 0.65 m. It is possible that there is a mistake in either your calculation or in the book. I suggest double-checking your calculations and also consulting with your instructor or classmates to see if they have a different solution. It is also important to note that there could be other factors or variables that were not mentioned in the problem, which could affect the final answer. As a scientist, it is important to always question and verify information, so I encourage you to continue exploring this problem until you have a clear understanding of the solution.
 

What is the length of wire?

The length of wire refers to the distance between two points on a wire, typically measured in meters.

How is the length of wire measured?

The length of wire can be measured using a ruler, tape measure, or other measuring tools. It can also be calculated by counting the number of loops or turns in a wire.

What factors affect the length of wire?

The length of wire can be affected by factors such as temperature, tension, and material composition. Changes in these factors can cause the wire to stretch or contract, altering its length.

Why is the length of wire important?

The length of wire is an important measurement in various industries, including electrical engineering, telecommunications, and construction. It is used to determine the amount of material needed for a project and to ensure the proper functioning of electrical and communication systems.

Can the length of wire be shortened or lengthened?

Yes, the length of wire can be altered by stretching or compressing it. However, this may affect its properties and performance, so it is important to consider the intended use of the wire before making any changes to its length.

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