User:CWilliams
From MariachiWiki
Christian Williams is a philosophy major in his senior year at Stony Brook. He's had a love for science for just about his whole life, but has always been pretty bad at math and physics. Because of this, he prefers to study science outside of the academic setting by reading books and articles and pontificating on their meanings and implications. His favorite fields of science are quantum mechanics and cosmology. Christian has also been involved with the organization NYPIRG since his junior year, devoting his time and efforts primarily to its environmental campaign, but also to other campaigns as well such as voter registration or higher education.
Unfortunetly, Christian also belongs to the unlucky horde of people who must have a job, so he works at the very chic and luxurious Stop and Shop. Its a mindless job, but it helps to pay the bills. It also allows him to enjoy a wonderful natural high when he finally gets to punch out for the day and escape into the fresh air. When he isn't working or reading up on the latest science news, Christian likes to spend his time listening to music and playing the guitar. He also enjoys reading novels, playing video games, taking pictures, going for walks and watching movies.
It has been reported that Christian also has the ability to grow very fine moustaches. There have been reports that his moustache enables him with the gift of flight, while other facial hair configurations lead to different powers. These reports are largely undocumented however, and are thought to be mere rumors.
This is a link to an article about what could be the future of waste management. (Its way cool if you ask me) http://www.popsci.com/scitech/article/2007-03/prophet-garbage
Contents |
Sept. 3
In the first week of class, we were given some background information on cosmic rays, such as their sources, their energy and their quantity. We also were introduced to two methods of detecting them. The first involved a tank in which alcohol was allowed to evaporate, which was on top of a container of dry ice. As the alcohol evaporated, it tried to form clouds at the bottom of the tank, but instead formed into a mist. When a light was shone on the tank, we were able to see the trails of the rays as they passed through the mist. The second method involved the use of electronic detectors. As the cosmic rays passed through the detector, a signal was sent to a computer that would provide a picture of how long it took to pass through the detector and how much energy it had. The class broke up into groups and attempted to gain an understanding of how the detectors worked by calibrating a detector against two others. Our goal was to find the voltage at which there were the highest number of coincidences of detection with the lowest amount of background noise.
This is a link to the data that was collected: [[1]]
Sept. 10
During the first part of the class in the second week, Mr. Stuckey taught us in greater detail about how to manage and edit our wiki pages. We learned how to place images in certain alignments on the page, how to create headings, and how to upload images or media. Dr. Dima then gave the class some information on how to use some of the functions of Microsoft Excel. He also showed us how to make a graph from the data that we had collected.
After the tutorials were completed the class broke up into groups to work with the detectors. Our first task was to figure out the voltage at which the detector would run at the highest efficiency with the lowest level of noise interference. Based on the data from Chart #1, our group determined that the optimal voltage was 4.8 volts, which was surprising for us because we were expecting that the voltage would have to be much higher.
After making the calibrations, our group then ran 30 trials at intervals of 10 seconds and recorded the number of counts for each trial. As shown in Chart #2, the number of counts that were recorded greatly fluctuated from trial to trial. From this data we were able to calculate that the average number of counts for the 10 second trials was about 171.
Our group then ran five more trials at 60 second intervals. Chart #3 depicts the data from those trials, which reveal a similar zig-zag pattern of counts. The average number of counts for these trials was about 1034.
Chart #4 contains the data of the number of counts for which there was a threefold coincidence.
Sept. 17
In the beginning of today's class, Dima taught the class the types of error that can be encountered when running experiments. He spoke about how random errors tend to follow a bell curve, with 68% of the measurements falling within the range of FWHM, or Full Width Half Maximum. He also taught us how to calculate the approximate amount of error in an experiment. Dima then showed us how to create graphs in Excel that display the amount of deviation that is allowed for in a result due to error.
After the lesson the class broke up into groups. Our task was to learn if the relative positions of the detectors had an effect on the rate of three-fold coincidences. To do this, our group ran several trials in which we moved the middle detector more and more out of line with the other two, as depicted in the beautiful Picture #1, until we eventually removed the detector completely from the stack and placed it on the floor.
After we ran the trials and contrasted the resulting number of three-fold coincidences with those of the initial unaltered setup, we found that as the amount of total surface area that all three detectors shared decreased, the number of coincidences decreased as well. We also noted that, while sparse, there were still instances of coincidence even when the middle detector was placed on the floor away from the other two that remained on the table.
We then plotted the data in Excel, showing the relationship between surface area and the rate of coincidences, as well as the slope (Chart #5).
Sept 24
This week, our group was assigned the task of determining how the solid angle produced by the locations of the detectors affects the rate of 3-fold coincidences among the detectors. To do this, we worked with the detectors that are attached to the wall behind the seats. The top two detectors always remain in place at approximately the height of the ceiling but the third detector is attached to a pulley system which allowed us to position the third detector at whichever height we wanted.
Our group then decided on several heights for the third detector and we ran trials to record the rate of coincidences. The purpose of changing the location of the bottom detector was to limit the angles at which the detectors could detect an instance of 3-fold coincidence; the lower the detector the smaller the angle. See Image #1. Our group also had to take into consideration what is called the solid angle, (image Image #1 in three dimensions) since the cosmic rays could be coming from any direction.
The results of the trials that were run coincided with our expectations, those being that the further the bottom detector was from the other two, the lower the rate of 3-fold coincidence.
After discovering a mistake that we had made in our original set of measurements (which resulted in data that was far outside the acceptable range of percent error) we were finally able to make a graph of the rate of 3-fold coincidences relative to the solid angle. See Image #2.
Oct 15 & Oct 22
On this fine autumn evening, class began with a recapitulation of the work that had been carried out by the various groups two weeks earlier. After reviewing our endeavors, the groups split off to work on new tasks. Dana and I were on a mission to determine the speed at which cosmic rays travel.
To do this we knew two things: that we had the use the formula Speed=Distance/Time, and also that we had to make some measurements. Fortunetly for us, Dima was there to guide us along our way. Our first step was to familiarize ourselves with the oscilloscope which is a machine that displays on a screen when a detector is struck by a cosmic ray. It is capable of depicting multiple detectors at once, and also shows the time difference, in nanoseconds, between detections. Using this oscilloscope, Dana and I ran two trials-one trial with the bottom detector directly underneath the top two, and one with the bottom detector at its lowest position. We then divided the distance between the detectors (265cm) by the time differences (5 nanoseconds) and came to the conclusion that the cosmic rays were traveling at about 1.75 times the speed of light. Our first thought was that we had made a significant discovery in the world of physics, having found proof that a substance can in fact travel at greater than light speed. However, we were wrong. What really happened was that we messed up.
So in order to get back on the right path, Dima helped us understand where we made our mistake. Our first problem was that we only had two trials to compare. When trying to make an accurate measurement, it is always better to use several trials, rather than just a few. Using the oscilloscope, we recorded the time difference between detections with the bottom detector in both the highest and lowest positions. After that we determined the average time difference (in nanoseconds) and then subtracted one average from the other, and used that number as Time in Speed=Distance/Time, and found that the cosmic rays were traveling at a speed somewhere in the neighborhood of 30.8cm/nanosecond. While this is still slightly higher than the speed of light, it is much closer than our original estimate.
After completing this, our next task was to determine the amount of error in our calculations. Applying the appropriate formula, we found that the relative error in our time measurements was about 8.2%. We also concluded that the relative error in the distance measurement was about .56%.
Using the data, the team was able to produce Graph #1.
On the 24th, each of the three groups in the class presented the findings that they had made with their own experiments. After presenting our information, our group was told that our graphs required error bars to be included with the data points because without them, it is difficult to be able to understand the worth of the data that is being represented. Graph #2 depicts the addition of error bars. It also has reversed the axes.
The next task that our group is set to take on is to improve the accuracy of our measurements by learning of new techniques we could use to reduce the amount of error. We also may be able to utilize new cool equipment that we don't even know about. We'll also look at the effect of increasing or decreasing the lengths of the wires that connect the detectors to the oscilloscope.
Check out these fine lookin numbers
Oct 29
In this week's class, our group took the next step in refining our measurements of the speed at which the cosmic rays travel. We did this by examining how the length of the wire that connects the detectors to the measuring apparatus (such as the oscilloscope or the computer) affects the data that is collected.
In order to do this we first had to take a bunch of measurements with the same length of wire that we used in our experiments from weeks past so that we could have data to compare to later measurements when the length of wire had been increased. Ryan completed this heroic task by recording the time difference between hits for 100 trials. After that was done we plotted the data in a histogram and produced Graph #1. As you can see, the data follows a bell curve which is what we had been expecting.
Mister Harry Stuckey showed us a trick that can be used in Excel to produce a little box that contains all kinds of information. So we made just such a box using the data from our hand-counted run and brought forth out of the void of non-being Image #1. Has there ever before been such a pristine display of kurtosis? Who can say?
After learning some new techniques and recognizing the approach of the class' end, our group added in 38 feet of wire between the detector and the oscilloscope and had the computer ran a bunch more trials. Once the data was collected we proceeded with the following calculations: we determined the time differences between hits to find the average time difference (=6.63E-08); then we subtracted the average time diff as determined by the computer in its earlier trials from the most recent set (=5.92E-08); then we used the formula for speed, Speed=Distance/Time, and divided the length of the added wire (38ft) by the diff between averages (=6.42E08); then we multiplied hat number by 12 in order to convert to inches (=7.70E09), then by 2.54 to convert to centimeters (=1.96E10). When all that was done, we had determined that the rays were traveling at around 65% of light speed, which I might say is quite speedy.
Next week we may try adding more wire to the mix to see what comes of it. The sources of inspiration for all these words can be found here:
The computer's first set of trials
Determing percent of light speed
Nov 5
Welcome to the wikipedic account of the events of the Fifth of November.
The first thing we did was perform a search of the Internet for information regarding the RG58 variety of cable. In particular we were trying to learn the speed at which a signal will travel through this type of cable so that we could see if it matched up with our past measurements. The two most common numbers we found were 65% and ~80% light speed, and since our own findings matched up with the former thats the one we went with. We decided that we ought to run some tests to see if we couldn't find out just how accurate our measurements were, and if we could improve that accuracy. Dima then had a discussion with us about standard errors and what they mean, how they can be determined and how they can be reduced. A good way to find answers to this kind of stuff is to run lots and lots of trials to produce lots and lots of data which we can use to (hopefully) produce a nice bell curve.
After chatting with Dima, our group understood that in order to increase the accuracy of our measurements by 50% we would have to take four times as many measurements as we did in the previous week, for a total of around 1600 measurements. We then used that data to produce Graph #1, which has a nice bell-ish curve thing going on.
Being the sillyheads that we are, we realized at just about the end of class that we never actually ran any trials that night with the cables at standard length, which was kind of a crucial step in our being able to gather any pertinent information about the measurements we made with the extra 38 feet of wire added in. Fortunetly for us, Dima was nice enough to keep the computer program running until the next day so that we could then have another set of data with which to compare our findings. And what's more, the always pleasant Ms. Haugh took it upon herself to go to the lab the next day and use the data to produce a histogram for the group, hereafter referred to as Graph #2. Since she had around 25,000 measurements to work with, and that's a bit more than was needed, Ms. Haugh used about 2000 of them in the Graph.
After gazing upon Graph #2, one will notice the very nice bell shape it has. One can also notice how very nicely approximately 68% of the data falls within one standard deviation of the mean. Image #1 contains some miscellaneous data from the trials.
Dana furthered proved her merit by using the data to find the percentage of light speed to be about 65%. Triumph!
This is the data gathered with the 38 feet of cable added in, and
This is the data gathered without the extra wire.
Nov 12
This week our group decided to rerun our original experiment that we first ran on Oct 5th, where we tried to determine the speed of the cosmic rays. To do this we had to take two sets of measurements, one with the bottom detector at the top position and one at the bottom. We had the computer take 1000 measurements at each position. Image #1 shows the results of when the detector was all the way up and Image #2 when it was all the way down.
We then computed the average time differences for each position to be 16.07 (at bottom) and 6.95 (at top), and found the difference between the two to be 9.11 nanoseconds. After that we remeasured the distance between the detectors when the bottom detector was at the low position and found it to be 259cm. Then, using the formula for velocity (Distance/Time1-Time2), we found the speed to be 29.49 cm/ns. We then had to calculate the standard error. Since we took measurements with the detector in two different positions, we had two different errors, so we had to figure out what the combined error would be by using this formula:
SQRT(E1^2 + E2^2)
So first we calculated our errors to be .27ns (at bottom position) and .12ns (at top position). Then after plugging them into the formula we found our combined error to be 3.34%, which, after doing some more calculations, comes out to a difference of plus or minus .95cm/ns. Since the speed of light is about 30cm/ns, we found that the cosmic rays are traveling at about 94% light speed.
This here is the numbers we used
Link back to PHY 315 main page: [[2]]
