# Physics 203 at Portland State 2014

### Site Tools

white_noise_project
A PCRE internal error occured. This might be caused by a faulty plugin

====== Differences ====== This shows you the differences between two versions of the page.

white_noise_project [2014/05/05 20:10]
wikimanager [Software and data analysis]
white_noise_project [2014/06/04 03:46] (current)
wikimanager [Software and data analysis]
Line 66: Line 66:
* sigma can be just a number (e.g. 1), or a cell someplace else containing the desired value       * sigma can be just a number (e.g. 1), or a cell someplace else containing the desired value
- //<color blue>​**Exercise 1**</​color>//:​ generate a column of 200 (and/or, separately, 20000) normally-distributed random numbers with sigma=1   - //<color blue>​**Exercise 1**</​color>//:​ generate a column of 200 (and/or, separately, 20000) normally-distributed random numbers with sigma=1
+    * //<color red>​**Question**</​color>//:​ How do we plot the input versus the output. ​ What is the input and what is the output?  ​
+      * //​**Answer**//:​ In this exercise, just create a column of random numbers. No need to plot yet.  --- //​[[nkuzma@pdx.edu|Nicholas Kuzma]] 2014/05/18 22:34//
- Plotting (using scatter chart) the output column versus the input column   - Plotting (using scatter chart) the output column versus the input column
* with main title      * with main title
Line 112: Line 114:
* $n_i$ is the observed (or predicted) number of occurrences in the //​i//<​sup>​ th</​sup>​ bin           * $n_i$ is the observed (or predicted) number of occurrences in the //​i//<​sup>​ th</​sup>​ bin
* $N$ is the total number of observations           * $N$ is the total number of observations
+    * //<color red>​**Question**</​color>//:​ I have the two histograms plotted. ​ For the quantitative comparison should I calculate the probability density for each bin?  for the exercise with $N=200$ would this be done by using the following equation: ${\text{probability density}}=$ $\frac{\text{#​ observations in bin}}{200\times 0.3}$ ?  I am having a hard time understanding if we need to calculate the predicted number in each bin.  Should I do this?  If so, how would I figure out how to do this?
+      * //​**Answer**//: ​ to compare "​experiment"​ with theory, you need either to convert your bin counts to the probability density (by dividing the counts by the total # of observations and by the bin width), and compare that to the theoretical curve, or, alternatively,​ convert the theoretical probability density to the predicted bin count, that is by multiplying the theoretical probability density by the total # of observations (200) and by the width of your bins (I guess, 0.3).  Then plot the two curves on the same plot, the theoretical curve using lines and the experimental bin counts using dots or other symbols. ​ --- //​[[nkuzma@pdx.edu|Nicholas Kuzma]] 2014/05/23 17:47//
- Save the exercises above for the "​Intro",​ "​Theory",​ and "​Methods"​ sections of your report   - Save the exercises above for the "​Intro",​ "​Theory",​ and "​Methods"​ sections of your report
* You can convert any screen content into an image that can be pasted into your report:     * You can convert any screen content into an image that can be pasted into your report:
Line 119: Line 123:
* Switch to the editing software (e.g. Word or Pages), and paste at the desired spot         * Switch to the editing software (e.g. Word or Pages), and paste at the desired spot
* on a PC, press ''​Alt''​ and ''​PrtScn''​ ("​Print Screen"​) at the same time, then release       * on a PC, press ''​Alt''​ and ''​PrtScn''​ ("​Print Screen"​) at the same time, then release
-        * Switch to the editing software (e.g. WordPowerpoint, or Paint)+        * Switch to the editing software (e.g. WordPowerpoint, or Paint)
* Paste at the desired spot         * Paste at the desired spot
* Crop the excessive margins as needed         * Crop the excessive margins as needed

-^ Figure 5. Examples of histogram plots in Excel   ​+^ Figure 5. Examples of histogram plots in Excel.  ​^
+| In the top figure, the theoretical curve has been scaled (multiplied by $N\Delta x$) to yield the predicted numbers of counts in each bin.  |

-
This is the detailed list of tasks to be accomplished:​ This is the detailed list of tasks to be accomplished:​
-  - Generate a single sine wave of amplitude $A=5$, phase $\phi=1.5\,​$rad,​ and frequency $\omega=2\pi\times ​4\,$Hz: +  - Generate a single sine wave of amplitude $A=5$, phase $\phi=1.5\,​$rad,​ and frequency $\omega=2\pi\times ​3.5\,$Hz:
-    * $V(t)=5\sin\,​(2\pi\,4\,​t+1.5)$ ​+    * $V(t)=5\sin\,​(2\pi\cdot 3.5\,​t+1.5)$ ​
* First, generate a column containing a grid of time values from 0 to several seconds with a step of 0.001 s       * First, generate a column containing a grid of time values from 0 to several seconds with a step of 0.001 s
* In the next column, type a formula containing the above equation and drag it by the corner all the way down       * In the next column, type a formula containing the above equation and drag it by the corner all the way down
Line 160: Line 165:
* Try to offer your intuition as to why adding (averaging) several pure sine waves results in such a drastically different histogram         * Try to offer your intuition as to why adding (averaging) several pure sine waves results in such a drastically different histogram
* If intrigued, try to experiment with fewer than 200 sine waves. At what point does the dramatic change of the histogram happen?         * If intrigued, try to experiment with fewer than 200 sine waves. At what point does the dramatic change of the histogram happen?
+    * //<color red>​**Question**</​color>//:​ I need to figure out what is wrong with my frequency graph (average of 200 sine waves). I have re-plotted it again, checked my formulae, and I still am unable to find any error.  ​
+      * //​**Answer**//:​ I looked at your file, and the data is actually correct. The problem is with your plot.  Do you know how to change the axis range? As it is now, you are "​zoomed in" too much on your figure: the //x// axis is only from 0.1 to 0.3 s somehow, and the //y// axis is from $-0.02$ to $+0.02$. Basically it is blowing up a tiny little aspect of the plot, and not showing the whole picture. ​