User:RDoyle
From MariachiWiki
I enjoy writing and playing bass guitar because creative outlets help keep us sane. I recently started a website for all the varied creative efforts of my friends, and their friends, and so on, called Circle of the Word. We've got writing, art, music, film and animation. Feel free to check us out and keep in mind that submissions are always welcome.
I'm attending Stony Brook full time and working at a paint store full time as well, so I don't have a lot of free time, but when I do get a moment I enjoy reading and watching movies. Lately, my favorite author has been Kurt Vonnegut and my favorite writer/director has been Wes Anderson. Thanks to the careful efforts of my girlfriend, Lauren, I am becoming more and more of a museum person as well.
This picture of me was taken by Lauren in Scranton, Pennsylvania during a torrential downpour. We were on our way home from a trip to Buffalo and Niagara Falls this summer, when we made a detour to find the home of "The Office." It took over an hour to find this small Dunder Mifflin sign, I got completely soaked and the picture came out pretty awful, yet I can't help but laugh every time I look at it.
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September 10th 2008
First we repeated the efficiency experiment. The detector we tested turned out to perform better at a voltage that was significantly lower than what we expected based on last week's findings. We learned the unique nature of each of these detectors, resulting from the fact that they are hand made pieces of equipment. I had not realized that they each have their own personality. To the right is a graph of our results:
Once we had selected a voltage for the center detector, we proceeded to run thirty ten second trials and five sixty second trials to observe the rate at which each detector counted. Below is a graph of what each detector counted per second:
The detectors averaged 383 hits per second. But, while detector 1 averaged 144 hit per second and detector 2 averaged 171 hits per second, the third detector came in significantly higher with an average of 834 hits per second. It seems detector three was much "noisier" then the other two detectors. It is also interesting that after the first six trials it seemed to calm down a bit. Still, detector three registered a count significantly higher than the other two detectors. This skews the scaling so that detectors one and two seem to be pretty consistent. Yet looking at one of these alone, in this case detector two, reveals a rather large variation in the counts over the thirty ten second trials.
This variation in one detector alone, plus the more pronounced differences between detectors made me realize how important the coincidence rate is. It seems that the only way to determine what part of the count is from noise and what is actually cosmic rays is through measuring the coincidence rate. Below is a graph showing the three-fold coincidence rates from these trials:
On average the three-fold coincidence rate measured 16 events per second. There was some variations between the trials, but what is interesting is that in the last five trials, which were the sixty second trials, the numbers are much more consistent. It appears that, along with measuring the coincidence rate apposed to the count of a single machine, a longer trial also contributes to more accurate data.
Here is our raw data from Sept. 10
September 17th 2008
First we learned how to calculate the standard deviation for our findings. This translates to error bars on the graphs. Error accounts for the fact that our measurements can not be considered completely accurate. Our findings are therefore the observed data plus or minus the standard deviation. The probability for the actual event falling into the observed data plus or minus the standard deviation is 68%.
After we learned how to account for error, we performed an experiment to see how altering the amount of overlapping surface area the detectors shared affected the three fold coincidence counts. In order to register a three fold coincidence, a cosmic ray must pass through all three detectors. By sliding the middle detector out (very carefully), we took measurements at three different positions as well as the control sample of complete overlap. We also took a fifth measurement with the middle detector completely removed from in between the other two detectors and placed on the floor. Dana drew this picture showing the process (I think I'm the one on the right).
Plotting the data shows, as we suspected, a slope demonstrating a direct relationship between the threefold coincidence rate and the surface area the three detectors shared. While the control measurement came in at 16 counts per second, as we decreased the surface area the detectors shared the rate of three fold coincidences dropped accordingly. The data including the error bars only touches the trend line at one of the measurements. This probably means that we took incorrect measurements of how much area the detectors shared. There was some confusion as we propped up detectors with garbage cans and shelving brackets and looking back I can see how a detector may have been moved a bit after we had measured its position.
Something interesting occurred in our fifth trial. Just out of curiosity, we took the middle detector completely out from between the other two detectors and placed it on the floor next to the table. We expected to get a count of zero in this position, but in actuality we got a rate of about one hit every two to the three seconds. We all found this surprising at first, but we realized that cosmic radiation could pass through all three detectors, even though they were not touching, if it was traveling at a certain angle.
September 24th 2008
After our strange findings at the end of class on the seventeenth, our group decided to find data on the angle at which the cosmic rays are traveling. Do accomplish this we used the apparatus where two detectors are set at the height of the ceiling and a third detector can be moved to adjust the height. By altering the distance between the detectors we alter the solid angle of the sky we are measuring. If the majority of the cosmic radiation passing through the detectors is coming straight down (which I realized last week was how I've been picturing it in my head) then there should be little variation in the rate of hits as the solid angle is changed. But we discovered that, while the three detectors were touching we measured a coincidence rate of 13.7, when the movable detector was all the way down, or 278.8 cm away from the top detectors, the coincidence rate fell significantly to .533. This shows that the majority of the cosmic radiation is actually not coming straight down. While this goes against my original conception of cosmic radiation, it makes sense scientifically as well as intuitively. By increasing the solid angle measured, we increase the area of the sky where cosmic radiation can be coming from. While I once thought that this radiation was hitting me in the crown of my head, I now realize that it is coming from many angles and hitting me right between the eyes as well.
The astute observer will notice that next to the listing of this course there are parentheses stating "For non-physics majors." Well, that would be me. The twenty-fourth was a rough night. Our first batch of measurements were off because we did not realize that the bottom detector was actually on an angle, causing the distance and therefore the solid angle calculations to be wrong. We regrouped and took a quick second batch of readings more carefully. Then we learned that calculating solid angle is pretty complicated mathematics. Still, through teamwork and Dima's nearly infinite patience, we managed to persevere and proudly present this graph:
The entirety of our data can be viewed here. I think we may need to take more measurements at smaller distances, because originally we did not realize the relationship of distance to solid angle. Still, there is a clear trend developing and it appears that cosmic radiation is coming from many locations and traveling at various angles.
It would be interesting to compare our data to the group who measured direction, since the two experiments are closely related. There may also be a relationship between our data and the group's who worked with Cosmic Chris. They found that as they went higher in the building the rates increased accordingly. It could be that the amount of radiation that is coming more or less straight down is being filtered out by the building, while the radiation traveling at angles that pass through less of the building is more likely to reach the detectors. This depends on whether it is the altitude which is causing the change in the rates in their experiment or if it is actually the number of floors between the detector and the sky which is causing it.
October 17th 2008
Unfortunately, I was sick on the night of the fifteenth, but Dima was kind enough to meet with me on Friday afternoon and allow me to catch up. With Dima's help, I recreated the experiment my group did on Wednesday night. We had decided to measure the speed at which the cosmic rays were traveling and measure them we would. I used the same set up we used to measure solid angle, this time connected to the oscilloscope. The oscilloscope allows one to view the pulses the detectors are transmitting. The shape and amplitude of the pulse are shown, but more importantly for this experiment, the time of each pulse is shown as well. By measuring the time difference between two pulses during a coincidence when the detectors were touching and then by taking the same measurement when the distance between the detectors was increased, it was possible to determine the speed of the cosmic radiation. The speed of the cosmic radiation is calculated by dividing the change in the distance by the change in the time.
While this sounds very simple, it is in fact difficult to measure the time between the pulses on the oscilloscope. No matter how careful one is and no matter how much eye strain one is willing to undergo, the time aspect for each pulse can only be measured within an error range of one nanosecond. Since each measurement of the time between the pulses requires establishing the time for two separate pulses, each reading has a margin of error of two nanoseconds. Now in most day to day activities, getting something within two nanoseconds would be pretty good to say the least, but when measuring cosmic radiation, two nanoseconds can make a big difference. Taking multiple measurements can reduce the impact of this error, but it still can not be completely eliminated due to the nature of the oscilloscope. Over multiple trials, the error (2 ns) is divided by the square root of the number of trials, giving us an error of .447. Here are the measurements.
With the movable detector all the way up and touching the other detectors, there was an average difference of 6.8 ns between the pulses. When I brought the movable detector all the way down to a distance of 258 cm, the average difference between the pulses grew to 15.4 ns. This gives the speed as 29.99 cm/ns, but with a cumulative error of 2.19 cm/ns. The slope of the graph, with measurements taken at three different points, has a slope of 29.95 cm/ns, which reinforces the findings. This is to say that the cosmic radiation is moving within about 2 cm/ns of 30 cm/ns, which represents the speed of light.
While it is impossible to say exactly how fast the cosmic radiation is traveling with this equipment, we can say confidently that it is moving very close to, if not exactly at, the speed of light.
October 29th 2008
To better understand how to increase the accuracy of our speed measurements, we set about examining the speed at which signals travel through the wires which connect the detecters to the oscilliscope. To do so we examined the time difference between pulses.
First, we entered into the ancient battle of human vs. machine. We took a set of measurements by hand, then had the computer take a set of measurements. By plotting the two sets of data as histograms and by using a function of Excel that Harry was kind enough to show us, we compared our accuracy to the computer's.
The Computer had a lower standard error because it took more than three times as many measurements. Our data has a lower standard deviation and variacne though. This shows that our taking data by hand was more accurate than the computer. That's right, we won! The catch is that the computer took much more data in less time, so from an effeciency stand point the machines win. Our Data. Computer's Data.
Since the computer could reduce standard error by taking many more measurements faster than we were capable of, and considering that we spent most of the class figuring out who won the competition, we decided to us the computer to gather the data which would allow us to determine at what speed the signals were travelling.
We added 38 feet of wiring between the oscilliscope and the bottom detector. By taking the Data from the two sets of the computer's measurements and using the magic of math we found that the signals were moving through the wires at 19.56cm/ns plus or minus .99, or 65.3% the speed of light.
Novemeber 5th 2008
Our first task was to discover if our data from last week was any good. We had found that the signals between the detectors and the oscilliscope travel through the wires at 65% the speed of light. The true value could be determined simply by searching the internet for the specifications of RG58 we were using. It turned out to be, like so many things in life and this class, a bit harder than we had imagined it would be. After a lot of searching and heavy sighs we found a few sites claiming the magic numbers of 65 and 66%. Victory! But there were a couple other sights saying it was 80%. Who to believe? Were we right, was eighty percent simply a case of blatant false advertising? Only time would tell.
We sat with Dima and discussed how we could make our data more accurate. The answer was more data, more data, more data. We learned that the percent error is reduced by the square root of the increase of the total number of counts. So to get the data twice as accurate, you'd have to take four times as many measurements.
So, with the help of the computer, we took a whole lot of measurements. We plotted the data in a histogram and ran Excel's handy stats package and were very happy with what we found:
A nice looking bell curve and a very low standard error.
We were tired and a little delirous from watching the counts add up, but we had done it and the standard era had dropped significantly. We were elated and it was time to go home after a long night. But wait, we completely forgot to take a second set of data with the 38ft of wiring removed in order to calculate speed. Doh!
We set the computer to collect data as we left and Dana was kind enough to go in the next day to stop it and analyze the data.
Dana took the next step and calculated the percentage of the speed of light that the signals were travelling. We found that the signals moved at 19.75 cm/ns plus or minus .4, or 66% the speed of light.
Next week we shall apply the lessons we have learned to measuring the speed of the cosmic radiation with more accuracy.
Novemeber 12th 2008
This week we decided to remeasure the speed of the cosmic radiation. Armed with the knowledge we aquired from measuring the speed at which the signals travel through the cables, we hoped to get a more accurate reading with a lower percent error.
We used the same set up we had used originally, but only took measurements at the highest and lowest positions. Since the computer can calculate the time difference between pulses much faster than we are capable of doing by hand, we set the computer to record around one thousand events at each position. As we learned from the solid angle experiment earlier in the semester, the coincidence rate drops significantly as the detectors are moved farther apart, so we estimated that 1,000 events at each position was close to the maximum we could manage to obtain and process within one class period.
We plotted the histograms for each set of data to get a sense of our distribution and standard deviation:
We found that a difference of 259.72 cm between the two detectors cuased a change of 9.11 ns (with an percent error of 3.34%) between the pulses. This gives us a speed calculation of 28.49 cm/ns plus or minus .95. Here's the data and calculations.
As we waited for the computer to collect the data, I had an idea: That while it would be very difficult to prove that the radiation were moving at the speed of light, it would be easier to prove that they weren't. When we had finished collecting data and making calculations to arrive at 28.49 cm/ns plus or minus .95, I thought we had proven that the cosmic radiation was travelling at a speed slower than the speed of light, 30cm/ns. However, Dima showed me on that statistically, if the cosmic radiation was travelling at the speed of light, we should find them moving at our figure about sixteen percent of the time, since the speed of light is less than two standard errors from our measurement. Since images speak louder than words, here is an example of the bell curve:
