Abstract

In order to determine the speed of a muon, we set a cosmic ray detector with 4 counters and varyfing distances to measure the time of flight between the counters over the period of 9 days. We calculated the speed to be 2.96 x 10^8 m/s, with a range due to uncertainty of 2.94 x 10^8 m/s to 2.97 x 10^8 m/s.

When you are searching for the data make sure you unselect the blessed option under the advanced search. The distances between the counters can be found in the comments section of each data file.

Introduction

Using detector ID 6865, beginning Tuesday, May 17th and ending Wednesday, May 25th, 2016 at Medford High School in Medford, MA students collected data with various separation distances between counters 1 and 4. Counters 2 and 3 were also used to provide a fourfold coincidence. Over the course of the week of data collection, our counters collected the time of flight of each muon, the number of events (hits), and the standard deviation. Using this data, we calculated the speed of a muon in our frame of reference.

Procedures

1. Set up the 4 counters on top of one another separated by a certain distance.
2. Measure and record the distance between the counters.
3. Measure the geometry of the set-up in relation to the GPS.
4. Start data collection, making sure coincidence is set to 4.
5. Upload data after at least 12 hours.
6. Repeat steps 1-5 changing the distance between the counters. When changing distance, make sure the change is at least 1.25 ft in order to account for the 1.25 ns clock in the board. 
7. Analyze collected data by calculating time of flight studies between counters 1 and 4. 
8. Using the data from the time of flight studies, graph time of flight vs. separation distance. Calculate the slope of the line of best fit of this graph. The units of the slope will be in ns/m. To calculate the speed of a muon, take the inverse of the slope yielding units of m/ns. 

Click here for pictures of the setup.

Results

Data table

In our data table we have our separation values. This is how far apart the top and bottom counters are. Our shortest separation was 1.57 meters, and our largest was 2.49 meters. We then have our mean time of flight. Since we set the counters to 4 fold coincidence this was how long the muon took to go through all of our counters. Our fastest time was 5.24 nanoseconds, and our slowest time was 9.9 nanoseconds. Next we have the standard deviation, then N (number of hits) and we used our standard error for the error bars on our graph. 

To get the speed of the muon from the calculated slope, make sure to take the inverse of the slope.

Speed of muon:

- From logger pro: 2.96x10^8 m/s

- From hand-drawn graph: 2.79x10^8 m/s

Here is a sample of some of our data: 

Discussions & Conclusions

After carefully analyzing our data and taking into account the uncertainty, we calculated the range for the speed of a muon. Without taking into account any error, the speed of the muon was calculated to be 2.96 x 10^8 m/s from Logger Pro. Our second calculation, taking into account the +/- 0.02112 uncertainty on the slope and 3 significant digits, we calculated a maximum speed of 2.97 x 10^8 m/s and a minimum speed of 2.94 x 10^8 m/s. 

We repeated this process with a hand drawn graph and an average value of 2.79 x 10^8 m/s. When using the error bars to find the max/min slope, we got a maximum slope of 3.9 ns/m, yielding a minimum speed of 2.56 x 10^8 m/s. We got a minimum slope of 3.29 ns/m, yielding a maximum speed of 3.03 x 10^8 m/s. 

Bibliography