I am doing a project analysis and need some help with errors

In summary, the conversation discusses the use of microwaves in a wave guide to measure its width via standing waves. A graph was plotted and a formula was derived to calculate the width using the slope and x-intercept. However, the speaker needs help in determining the error in their experimental value. Gauss' error laws and a regression package can be used to calculate the error in the slope and x-intercept.
  • #1
foxen
1
0
Basically, I have used microwaves in a wave guide to measure the width of the guide via standing waves. This led me to plot a graph of 1/wavelength in the guide^2 vs 1/wavelength^2 in air.

The graph showed the following formula; y = 1.0741x + 455.08 with an R^2 value of 0.9979 from 5 points.

This enabled me to calculate the width of the guide using the following formula; 1/2*width^2 = c. which came out as 2.34e^-2m.

So far a very good result, as when I measured the guide it had a width of
2.3e-2m +/- 0.05e^-2.

The problem is that I now need to work out the error in my experimental value of a. Which is obviously a product of the accuracy of the slope of the graph. How should I proceed? Any help would be appreciated.
 
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  • #2
You need Gauss' error laws:

Given a formula [tex]z=x^{\pm a}[/tex] ([tex]a[/tex] a constant) then the error in [tex]z[/tex] is [tex]\frac{\Delta z}{z}= |a|\frac{\Delta x}{x}[/tex]


and given a formula [tex]z=b.x[/tex] ([tex]b[/tex] a constant) then the error in [tex]z[/tex] is [tex]z=a.\Delta x[/tex]

You can combine both of those to get the error. To get the error in the slope and x-intercept in your graph (provided you've added some kind of linear trendline to it) then you need to use a regression package (one comes as standard with MS Excel) and that will give you the data you need.
 

What is the purpose of a project analysis?

A project analysis is used to identify and evaluate potential risks, errors, and areas for improvement in a project. It helps ensure the project is completed efficiently, effectively, and within budget.

What are common errors that can occur in a project analysis?

Some common errors in a project analysis include incorrect data, misinterpretation of data, biased analysis, and not considering all relevant factors. These errors can lead to inaccurate conclusions and hinder the success of the project.

How can errors be avoided in a project analysis?

To avoid errors in a project analysis, it is important to thoroughly review and verify all data and analysis methods. It can also be helpful to have multiple individuals review the analysis to catch any potential errors or biases.

What are the benefits of conducting a project analysis?

Conducting a project analysis can help identify potential issues and risks early on in the project, allowing for adjustments to be made before they become costly problems. It can also help improve the overall efficiency and effectiveness of the project.

Can project analysis be applied to any type of project?

Yes, project analysis can be applied to any type of project, including scientific research, product development, and business initiatives. It is a valuable tool for identifying and addressing potential errors and risks in any project.

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