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

1. Oct 22, 2009

### foxen

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.

2. Oct 25, 2009

### Zorba

You need Gauss' error laws:

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

and given a formula $$z=b.x$$ ($$b$$ a constant) then the error in $$z$$ is $$z=a.\Delta x$$

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.