Cerenkov Radiation : a water analog

ACTIVITY MODULE WATER ANALOG

Overview

Abstract: Students will gather and analyze data from a shock wave in water. (The wave following an object moving in water) They will use this data to understand the Cherenkov radiation as a shock wave produced by a muon traveling in ice. Furthermore, the experiment should help students understand how the AMANDA project can determine the path of the muons and therefore, extrapolate the direction of the source of neutrinos.

Rationale: To design an experiment, which helps students visualize how AMANDA reconstructs the path of muons through the Antarctic ice cap.

Grade Level/Discipline: Physics Class, Grades 11& 12

Objectives:
Use trigonometry in a practical experiment to increase scientific knowledge
Gather and analyze data from a shock wave in water
Use this data to understand the Cherenkov radiation as a shock wave produced by a muon traveling in ice

Connection To Curriculum/Teacher Preparation for Activity:
Standards:
WI Standards for the Water Analog Activity

A.12.3 Give examples that show* how partial systems*, models*, and explanations* are used to give
quick and reasonable solutions that are accurate enough for basic needs
A.12.6 Identify* and, using evidence* learned or discovered, replace inaccurate personal models*
and explanations* of science-related events
A.12.7 Re-examine the evidence* and reasoning that led to conclusions drawn from investigations*,
using the science themes*
A.8.2 Describe* limitations of science systems* and give reasons why specific science themes* are
included in or excluded from those
A.8.6 Use models* and explanations* to predict* actions and events in the natural world
B.12.4 Show* how basic research and applied research contribute to new discoveries, inventions,
and applications
C.12.3 Evaluate* the data collected during an investigation*, critique the data-collection procedures
and results, and suggest ways to make any needed improvements
C.12.4 During investigations*, choose the best data-collection procedures and materials available,
use them competently, and calculate the degree of precision of the resulting data
H.12.6 Evaluate* data and sources of information when using scientific information to make decisions
H.12.7 When making decisions, construct a plan that includes the use of current scientific knowledge
and scientific reasoning

Materials List:
Tape measure (50 meters in length)
Small boat with pointed bow(weighing approximately 2 kg)
8-10 stopwatches (at least to the tenth of a second)
Fishing line and a means to reel in the boat
16 Bobbers weighted to the bottom of the pool (optional - helps students visualize passing wave)
Videocamera, tape and VCR (optional)
Pool (or other relatively waveless body of water)

Pre-activity set-up:
Before students show up, teacher should place bobbers at regular intervals in the pool if you're doing the extension activity. Remember to reserve pool. If possible, use the timing equipment from a swim meet. Data gathering will probably take 20-25 minutes for the first part of the experiment. Analysis will probably take 45 minutes.

Teaching Sequence
Engagement and Exploration:
Before the experiment, students should receive a brief explanation about shock angles.
Also, a quick review of the properties of waves, specifically, how velocity depends solely on the medium. This could be demonstrated before beginning the experiment in the pool.

Extension activity:
A square grid of 16 fishing bobbers could be set out in the pool. The class could then be split into two groups. Each group would pull a boat through the bobbers several times at different angles each time. Each group would be responsible for recording the bobber's location and time of disturbance and then give that information to the other group who would then have to predict the path of the boat using the given data. A videotape of the boat's path could be used to compare the calculated results with the actual results.

Probing Questions:
If we change the angle of the boat's direction, will all the detectors read the same velocity?

Student Assessment
Questions to begin discussion:
When the boat was pulled parallel to the detectors, did each detector find the same velocity?
When the boat was pulled at an angle to the detectors, what happened to the velocity between detectors?
In the experiment, what does the boat represent?
Could this data be used to infer the direction of the boat?
Questions to draw conclusions:
What relationship (equation) will be used to determine the shock angle?
How does the boat speed change the shock angle?
Could all of the detectors go off at the same time? If so give the condition.
Describe some of the problems that AMANDA must address to insure an accurate track.
Evaluation
Lab write-up with accompanying questions

Classroom Components
Background:
Check out websites using the keywords Cherenkov (alternative spelling Cerenkov). One example is
www.cakes.mcmail.com/cerenkov/cerenkov.htm
Another site containing an animation of a shock wave is
http://physics.csufresno.edu/akira/SR/Cherenkov.html
Finally, there are actual data from AMANDA with muon paths at
http://alizarin.physics.wisc.edu

Water Analog of AMANDA

Purpose: To design an experiment, which illustrates how AMANDA reconstructs the path of muons through the Antarctic ice cap.

Procedure:
1. Determine the speed of a wave in the pool by creating a disturbance on one side and measuring the time for it to travel across the pool. Measure the distance that the wave front travels in this time.
2. Position 6 to 8 people along the edge of a pool standing 1 to 2 meters apart. They should have their hand or foot just above the surface of the water in order to detect when the wave arrives.
3. Place a small toy boat in the water some distance behind the first person. Attach the boat to the rod and reel. Practice reeling in the boat along the line of people at a constant speed. Have the people on the side record times for a specific distance that the boat travels to practice their timing method and to insure that the speed of the boat is constant.
4. Measuring the shock wave. Have all persons start their watches at the same time. Begin pulling the boat at a constant speed. As the wake of the boat hits each person they should stop their watches. Record the time for each person.
5. Repeat the experiment for a number of trials keeping the boat parallel to the line of people.
6. Repeat the experiment for a number of trials with the boat moving at an angle to the line of people.

Calculations:
1. What is the speed of the boat?
2. What is the speed of the water waves?
3. What is the shock wave angle for your trials?
4. What is the angle of the boat with respect to the line of detectors?