The Effects of Frequency The Effects of Frequency Step Variation on H1 Range Step Variation on H1 Range Observations with the SRT Observations with the SRT

of the Sun in Transit.of the Sun in Transit.Robert KeeneyRobert Keeney

James McClintonJames McClinton

Renee SaucedoRenee Saucedo

Radio AstronomyRadio Astronomy

ST 562ST 562

Question:Question:

How will varying the frequency steps

effect the data quality received from

the SRT while observing a given

source?

Step Frequency GraphicStep Frequency Graphic0.04 MHz step – 0.02 MHz either

side of centerline frequency

25 total steps

1420

.5 M

Hz

1420

.52

MH

z

1420

.48

MH

z

1420

.56

MH

z

1420

.44

MHz

Step Frequency ChartStep Frequency Chart

1420.5 MHz

Step Values Frequency Range

0.005

0.01

0.02

0.04

0.08

0.16

0.32

1420.438 - 1420.563

1420.375 - 1420.625

1420.25 – 1420.75

1420.0 – 1421.0

1419.5 – 1421.5

1418.5 – 1422.5

1416.5 – 1424.5

Purpose:Purpose:

•To determine how the frequency graphs and the generated images of the source produced by the software are effected by varying the frequency step setting.

•To find if there is an optimum step setting.

•To determine the limits and constraints of the equipment and software.

Independent Variable:Independent Variable:

Frequency Step Value

Dependent Variables:Dependent Variables:•Frequency vs. Intensity Graph Resolution and Distribution

• Generated Images

Constants:Constants:•Time of Observation

•Source

•Software, Equipment, and Location

•Center Frequency

•Number of Steps on Either Side of the Center Frequency

•Number of Scan Points

•Interference Sources

Control: Control:

Default of 0.04 MHz to be taken every other reading.

Procedure:Procedure:1. Use an offset setting of 12 ° azimuth and 3° elevation,

centerline frequency of 1420.5 MHz and 25 channels throughout the procedure.

2. At 11:30 am on Monday, 19 July 04, take a baseline scan of the sun using the default settings. (Centerline frequency 1420.5 MHz, 25 channels, step setting 0.04 MHz.)

3. Perform subsequent scans varying only the frequency step settings to 0.005, 0.01, 0.02, 0.08, 0.16, and 0.32 MHz, with a baseline scan (0.04 MHz) in between each.

4. After each scan, take a screen snapshot of the generated image and accompanying graphs, as well as a screen capture of the frequency vs. intensity graph.

Results:Results:Baseline

Step 0.005 Step 0.01 Step 0.02

Step 0.04 Step 0.08 Step 0.16

Step 0.005Step 0.005

Step 0.01Step 0.01

Step 0.02Step 0.02

Step 0.04Step 0.04

Step 0.08Step 0.08

Step 0.16Step 0.16

BaselineBaseline

Step 0.04Step 0.04

Generated Generated ImagesImages

Baseline Step 0.005

Step 0.01 Step 0.02 Step 0.04

Step 0.08 Step 0.16 Step 0.32

Step 0.005Step 0.005 Step 0.32Step 0.32

Radio Astronomy Lesson Radio Astronomy Lesson PlanPlan

Measuring the Wavelengths, Frequencies, and Energies of

Laser Light by Diffraction Patterns

Objectives: Objectives: •Students will calculate the wavelength, frequency, and energy level of two separate laser beams by measurements taken from diffraction patterns.

•Students will demonstrate an understanding of the relationships among wavelength, frequency and energy level of electromagnetic radiation.

•Students will apply algebraic and trigonometric properties to investigate methods of calculating the wavelength of light from a given diffraction setup.

Prior Knowledge:Prior Knowledge:Students will be expected to:

•understand that light exhibits wavelike properties.

•be familiar with the concepts of single and double slit diffraction, and interference patterns.

•be able to solve for a given variable in an equation and determine an unknown angle using trigonometric ratios.

Materials:Materials:•Two lasers of different wavelengths

•Several diffraction gratings with different slit widths

•Stands

•Rulers and meter sticks

•Wall or screen on which to project patterns

•Long (pointy) stick to jab students with if they mess around with the lasers.

Procedure:Procedure:A lecture with a demonstration of a diffraction pattern setup to include the following:

Discussion on the significance of the terms of the equation:

Relate the quantities of wavelength and frequency through the equation:

Relate frequency to energy by the equation:

d

c

hE Where h is Plank’s Constant (h=6.63x10-34J•s)

Diffraction SetupDiffraction Setup

Diffracted Light Beams

Diffraction Grating

Projection Screen

Laser

Diffraction Grating

Diffraction Pattern DiagramDiffraction Pattern Diagram

Students will be tasked to derive the relationship

by use and understanding of this diagram. (and sharp, pointy stick persuasion if necessary)

1tan

Student Tasks:Student Tasks:Students will be broken into groups of two or three.

With the previous information, the groups will then be tasked to develop a method to determine the wavelength, and thus the frequencies and energy levels of each laser, using a meter stick and calculator.

The above will be repeated for two additional diffraction gratings of different widths.

They will additionally need to describe their method(s) in written form and record their results.

Once groups are finished, the compiled data will be presented to the class and the results compared to published data.

Teacher will monitor location of sharp pointy stick to assure it does not fall into the wrong hands.

99thth – 12 – 12thth grade Math Standards grade Math Standards•Strand: ALGEBRA, FUNCTIONS, AND GRAPHS•Standard: Students will understand algebraic concepts and applications.•Benchmark: Represent and analyze mathematical situations and structures using algebraic symbols.•Performance Standards

–Simplify numerical expressions using the order of operations, including exponents. –Evaluate the numerical value of expressions of one or more variables that are polynomial –Know, explain, and use equivalent representations for algebraic expressions.–Solve formulas for specified variables

•Benchmark: Understand patterns, relations, functions, and graphs.•Performance Standards

–Identify the independent and dependent variables from an application problem.

99thth – 12 – 12thth grade Math Standards grade Math Standards

•Strand: ALGEBRA, FUNCTIONS, AND GRAPHS•Standard: Students will understand algebraic concepts and applications.•Benchmark: Use mathematical models to represent and understand quantitative relationships.•Performance Standards

–Use a variety of computational methods (e.g., mental arithmetic, paper and pencil, technological tools).–Generate an algebraic sentence to model real-life situations.

•Benchmark: Analyze changes in various contexts.•Performance Standards

–Analyze the effects of parameter changes on these functions: –Solve routine two- and three-step problems relating to change using concepts such as ratio proportion.

99thth – 12 – 12thth grade Math Standards grade Math Standards•Strand: GEOMETRY AND TRIGONOMETRY•Standard: Students will understand geometric concepts and applications.•Benchmark: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.•Benchmark: Use visualization, spatial reasoning, and geometric modeling to solve problems.•Performance Standards

–Solve real-world problems using congruence and similarity relationships of triangles –Understand and use elementary relationships of basic trigonometric functions defined by the angles of a right triangle

•Guidance / Topics for Further Study–Trigonometry allows a student to consider periodic functions. –Students will be able to solve trigonometric equations–Students will be able to apply trigonometric functions to solve physical problems

99thth – 12 – 12thth grade Math Standards grade Math Standards•Strand: DATA ANALYSIS AND PROBABILITY•Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.•Benchmark: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.•Performance Standards

–Know the characteristics of a well-designed and well-conducted experiment.–Recognize sources of bias in poorly designed experiments–Understand the role of randomization in well-designed surveys and experiments.

•Benchmark: Select & use appropriate statistical methods to analyze data.•Performance Standards

–Understand the meaning of measurement data and categorical data, and of the term “variable.”–For bivariate data, be able to display a scatter plot and describe its shape.–Describe and interpret the relationship/correlation between two variables using technological tools

99thth – 12 – 12thth grade Science Standards grade Science Standards•Strand I: SCIENTIFIC THINKING AND PRACTICE •Standard I: Understand the processes of scientific investigations and use inquiry and scientific ways of observing, experimenting, predicting, and validating to think critically.•Benchmark I: Use accepted scientific methods to collect, analyze, and interpret data and observations and to design and conduct scientific investigations and communicate results.•Performance Standards

–Describe the essential components of an investigation.–Design and conduct scientific investigations.–Use appropriate technologies to collect, analyze, and communicate scientific data. –Convey results of investigations using scientific concepts, methodologies, and expressions, including: scientific language and symbols, diagrams, charts, and other data displays mathematical expressions and processes, clear, logical, and concise communication reasoned arguments.–Understand how scientific theories are used to explain and predict natural phenomena.

99thth – 12 – 12thth grade Science Standards grade Science Standards

•Strand I: SCIENTIFIC THINKING AND PRACTICE•Standard I: Understand the processes of scientific investigations and use inquiry and scientific ways of observing, experimenting, predicting, and validating to think critically. •Benchmark III: Use mathematical concepts, principles, and expressions to analyze data, develop models, understand patterns and relationships, evaluate findings, and draw conclusions.•Performance Standards

–Create multiple displays of data to analyze and explain the relationships in scientific investigations.–Use mathematical models to describe, explain, and predict natural phenomena.–Use technologies to quantify relationships in scientific hypotheses (e.g., calculators, computer spreadsheets and databases, graphing software, simulations, modeling).–Identify and apply measurement techniques and consider possible effects of measurement errors.–Use mathematics to express and establish scientific relationships.

99thth – 12 – 12thth grade Science Standards grade Science Standards

•Strand II: THE CONTENT OF SCIENCE •Standard I (PHYSICAL SCIENCE): Understand the structure and properties of matter, the characteristics of energy, and the interactions between matter and energy.•Benchmark II: Understand the transformation and transmission of energy and how energy and matter interact.•Performance Standards Interactions of Energy and Matter

–Understand that electromagnetic waves carry energy that can be transferred when they interact with matter.–Describe the characteristics of electromagnetic waves, including: origin and potential hazards of various forms of electromagnetic radiation energy of electromagnetic waves carried in discrete energy packets (photons) whose energy is inversely proportional to wavelength.–Know that each kind of atom or molecule can gain or lose energy only in discrete amounts.–Explain how wavelengths of electromagnetic radiation can be used to identify atoms, molecules, and the composition of stars.

99thth – 12 – 12thth grade Science Standards grade Science Standards

•Strand II: THE CONTENT OF SCIENCE•Standard I: (PHYSICAL SCIENCE): Understand the structure and properties of matter, the characteristics of energy, and the interactions between matter and energy.•Benchmark III: Understand the motion of objects and waves, and the forces that cause them.•Performance Standards: Motion

–Describe wave propagation using amplitude, wavelength, frequency, and speed.–Explain how the interactions of waves can result in interference, reflection, and refraction.–Describe how waves are used for practical purposes (e.g., seismic data, acoustic effects, Doppler effect).