Cosmic Ray Detector - Data Center Guided Tour Stop 1

Counting muons at different angles

Let's start by measuring muons at different incident angles. The cosmic ray detector is set up to do this at three angles:

1. horizontal (0 degrees)
2. 45 degrees
3. vertical (90 degrees)

About counting experiments and rates

It is important to obtain reliable measurements for the average number of muons that arrive in the detector in a certain time period (the count rate ). Let us begin by looking at some sample data.

1. In the top panel of the Data Center (it will open in a new browser window on your desktop) select a time period of roughly one hour by adjusting the From and To dates and times.
2. Set the Show option to Vertical (90 Deg) Count Rate Graph.
3. Set the number of intervals to 60 (so we have one minute per interval).
4. Now click on Retrieve Data.

You will see something like the following graph:

Example 1: 90 degree Count Rate, 1 hour, 60 one-min intervals

This graph shows the rate of cosmic ray muons going through the topmost and bottommost panels of the cosmic ray detector as it varies over time. You can see in Example 1 above that the rate starts out being 16 counts per minute, and the next minute the rate was 13 counts per minute (cpm). The minute after that, the rate was 14 cpm, and after that again 14 cpm. In the fifth minute the rate was 16 cpm again and then the rate fell to a low 9 cpm, and so on. Over this particular hour, the maximum rate ever measured was 24 cpm, and the lowest was 8 cpm. So, we see that the count rate fluctuates when measured over short intervals (one minute being a short interval). But if you squint at the graph (a time-honored tradition among physicists) you can also see that there is no particular pattern (especially if you compare with other hours). If you had to guess, you would say that the average rate is something like 14 cpm.

Fortunately, we don't have to guess.

1. Go back to the Data Center window.
2. Change the number of intervals in the top panel to 10 instead of 60.
3. Change the From date and time to be exactly 10 hours earlier than the To date and time
4. Click Retrieve Data again.

This time you will see something like this graph:

Example 2: 90 degree Count Rate, 10 hours, 10 one-hour intervals

Each interval is now 1 hour. The last interval in this graph is the same time period as covered by the entire Example 1 graph. We see that we were not far off in our estimate: the average rate for the entire hour was in fact about 15 cpm, not 14 cpm as we guessed. Again, this is for the data shown in Example 2 above: your results may vary.

But we also see that during previous hours, the rate was not the same as in the last hour. In the Example 2 plot above, it looks like the third hour had about the same rate as the last hour, but the other hours had a rate that was slightly higher. The highest rate was just over 16 cpm, and in fact the lowest rate was what we already measured, 15 cpm.

We can see a few properties that are common to all counting experiments.

1. When you average over longer time intervals, the spread of your measurements is smaller. In other words, there is less fluctuation.
2. Even though we lumped sixty measurements of one minute into one measurement of 60 minutes, other measurements of 60 minutes have a different result.
3. Therefore, when you count for longer time periods you come closer to measuring the "true" rate, although we can never be sure exactly what the true rate is.

Statistical uncertainties

You may note that the rates in the graphs are indicated with both a horizontal and a vertical line. The horizontal line is simply the length of time for that interval. The vertical line is what is commonly known as the error bar, although it doesn't indicate an error but rather a measure of the statistical uncertainty in that data point. In other words, the vertical line is a measure of how much one might expect the data to fluctuate around the measured value.

Count rates at different angles

Now, repeat the measurement (10 intervals of one hour) for the 45 Degree Count Rate Graph and the Horizontal (0 deg) Count Rate Graph. You will see something like this for the 45 degree count rates:

Example 3: 45 degree Count Rate, 10 hours, 10 one-hour intervals

and like this for the horizontal (0 deg) count rates:

Example 4: 0 degree Count Rate, 10 hours, 10 one-hour intervals

From this we can conclude that the count rate at 45 degrees is a little over 7 cpm for the last hour, and the horizontal count rate is a little less than 1 cpm.

So there is a clear pattern. You get different numbers of counts in the three pairs of counters. Do you have any guesses as to what could cause the pattern? We will come back to this in a later tour stop.

Tables

If we want to know more precisely what the rates are, reading numbers off the graphs is a little inconvenient and inaccurate. Therefore, there is an option to display the data as a table. Select Count Rate Table in the Data Center and click on Retrieve Data. You will see a table such as:

Table of Rate vs. Time

Interval Number	Date/Time	Rate (counts/minute)
		vertical (90°)	45 degrees	horizontal (0°)
1	Mon, 07 May 2001 12:51:00	16.017 +/- 0.517	6.617 +/- 0.332	0.850 +/- 0.119
2	Mon, 07 May 2001 13:51:00	16.333 +/- 0.522	7.233 +/- 0.347	0.850 +/- 0.119
3	Mon, 07 May 2001 14:51:00	14.950 +/- 0.499	6.783 +/- 0.336	0.933 +/- 0.125
4	Mon, 07 May 2001 15:51:00	15.667 +/- 0.511	7.117 +/- 0.344	0.933 +/- 0.125
5	Mon, 07 May 2001 16:51:00	15.867 +/- 0.514	6.750 +/- 0.335	0.833 +/- 0.118
6	Mon, 07 May 2001 17:51:00	15.883 +/- 0.515	7.433 +/- 0.352	1.033 +/- 0.131
7	Mon, 07 May 2001 18:51:00	16.083 +/- 0.518	7.300 +/- 0.349	0.767 +/- 0.113
8	Mon, 07 May 2001 19:51:00	16.233 +/- 0.520	7.400 +/- 0.351	0.917 +/- 0.124
9	Mon, 07 May 2001 20:51:00	15.567 +/- 0.509	7.383 +/- 0.351	0.917 +/- 0.124
10	Mon, 07 May 2001 21:51:00	15.033 +/- 0.501	7.233 +/- 0.347	1.033 +/- 0.131

From left to right, the table shows:

1. interval number
2. date and time corresponding to the (approximate) center of the interval
3. rate as measured in the vertical (90 deg) direction
4. rate as measured at 45 degrees
5. rate as measured in the horizontal (0 deg) direction

The notation 1.033 +/- 0.131 (for example) means that the average rate is 1.033 cpm and the uncertainty in that number is 0.131 cpm.

Go to Tour Stop 2
(Flux: a detector-independent quantity)