Lab Report #8

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ManualforElectromagneticWaves.docx

Temple University Physics

temple university physics

Electromagnetic Waves

In the first part of this lab, you will explore standing waves in a string, and in the second part, standing electromagnetic waves. We will see how the same physics describes both strings and electromagnetic waves. The data provided to you was collected using the procedures outline in this manual.

Learning Goals for This Laboratory:

· Know the various properties of waves including wavelength, frequency, speed, nodes and harmonics.

· Understand conditions for standing waves to form.

· Learn the length of scale of electromagnetic microwaves.

Part I. Standing Waves

In the first part of this lab, you will explore standing waves on a string. A string will be fixed at one end and vibrated by an oscillator at the other end. Waves travel outward from the oscillator and bounce back from the fixed end, interfering with the waves coming from the oscillator. For certain oscillator frequencies, this interference becomes regular and forms clear standing wave patterns in the string (with different numbers of segments depending on the frequency). The frequencies at which these standing waves form are called the natural or resonance frequencies.

To describe standing waves, we define a node, a point where the string does not move, and an antinode, a point where the amplitude is greatest. As you see from the diagram below: the length of one node-to-node section of the standing wave is equal to one-half of the standing wavelength: .

standing waves

By varying the driving frequency, you will produce standing wave patterns with different numbers of sections. You will measure the wavelength for each case and compute the product of the resonance frequency and the corresponding wavelength.

You will notice that the value of this product is always the same for standing wave patterns with different numbers of sections. This indicates that this product probably has an important physical meaning. Your research question is: what is the physical meaning of the product of the resonance frequency and wavelength?

1. Connect the vibrator to the Sine Wave Generator, hang the string over the pulley, and attach the mass to the end of the string as shown Fig. 1 below.

expb&w

Figure 1. Setup with string vibrating at the 3rd harmonic frequency.

2. Set the amplitude knob about midway, and then use the frequency knob to adjust the vibrations so that the string vibrates in several stationary segments. The pattern with one segment is called the first harmonic, that with two segments is called the second harmonic, and so on. The Figure above shows the third harmonic.

3. Fine-tune the frequency to obtain the largest amplitude you can while still maintaining a clear standing wave. Then record the frequency and wavelength in an Excel table similar to the one below. Take data for harmonics 2-8 before trying to find the first harmonic, also called the fundamental, because it is hard to find with exactness. Once you have the frequencies for the other harmonics, you will be able to estimate what the first harmonic should be, making it easier to set the oscillator.

Harmonic

Frequency (Hz)

½ (m)

(m)

(m/s)

1st

2nd

3rd

4th

5th

6th

7th

8th

4. Calculate the product of the frequency and wavelength. Record your results in the data table. Keep the appropriate number of significant digits.

Question 1. How does the product change with increasing frequency? Write a general equation for the product of the wavelength and frequency that best describes your observations.

Question 2. Review outside resources such as your text on the wavelength and frequency of electromagnetic waves and propose a physical meaning for the product of wavelength and frequency.

Part II. EM Waves

Watch the video here to see the Pasco microwave apparatus in use. The data provided to you was collected using this device and the procedure outlined below.

https://www.youtube.com/watch?v=nCAKQQjfOvk

Note that the data provided to you only uses the microwave receiver and transmitter, but in the video, you see the user insert a comb as well. The comb is a polarizer, preferentially absorbing waves oriented along the metal teeth.

The Pasco transmitter is an antenna containing a current oscillating at a frequency of 10.526 GHz. The current produces EM waves of the same frequency that radiate outward. The transmitter is a polarized source of EM waves, and in this experiment, you will determine the direction of polarization.

The receiver is also an antenna and collects only the microwave signal that is polarized along the attached horn’s long axis. When the wave is picked up by the antenna, a voltage is produced on the antenna, which is then amplified by circuitry in the receiver and displayed as DC current that varies with the intensity of the incoming microwave signal.

fig 24-41When the receiver is oriented at an angle to the incident polarization direction, only the component of the transmitted electric field that is parallel to the receiver, , will be detected (see figure at right). Because the intensity of EM radiation is directly proportional to the square of the electric field, the receiver’s meter reading should follow the relationship .

The purpose of the following activity is to test this prediction.

1. Arrange the equipment as shown below with = 0 and adjust the receiver current display controls for a nearly full-scale meter deflection.

2. Loosen the hand screw on the back of the transmitter enough so that it can rotate. Record the angle and meter reading at 15-degree intervals.

3. Plot the relative amplitude vs to see if the amplitude of the signal really does follow the predicted relationship. (Note: in Excel the function requires angles to be in radians, so either convert the values using a calculation, or the RADIANS function).

Question 3. Based on the graph and your data, what conclusion can be draw about the polarization direction of these EM waves? Answer with respect to the angle of the transmitter. Support your answer using your results.

Part III. The Wavelength of Microwaves

Because EM radiation propagates as waves, it should exhibit all the characteristics of wave motion such as reflection, refraction, diffraction and interference. Just as with the string in Part I, a standing wave forms between our microwave transmitter and receiver.

Let’s make a prediction: if we move the receiver away from the transmitter, we will see nodes at half-wavelength intervals.

Try the following activity to test this prediction and measure the wavelength of the radiation from the microwave transmitter.

1. Set up the equipment as in Part II. with the transmitter and receiver about 70 centimeters apart. Adjust the receiver controls to get a near full-scale meter reading. Slowly move the receiver along the metal arm, away from the transmitter while observing the meter reading.

Question 4. If there are standing waves as we predict, what should happen to the intensity reading as we move the receiver?

2. To reduce error, we’ll record the total distance for 5 wavelengths (11 nodes) then divide by 5 to get the wavelength. Reset the receiver to about 70 cm and slide it away from the receiver until you reach the first node; record its position. Continue sliding the receiver away while recording the positions of the next 10 nodes. Find the total distance traveled between nodes 1 and 11 and divide by 5 to find the average wavelength. Record these calculations and your final wavelength for your report.

Question 5. Show why 11 nodes corresponds to 5 wavelengths.

3. The nominal frequency of the microwave radiation from this transmitter is 10.525 GHz. Calculate the average speed of propagation of the EM radiation using the relationship . Record your result in m/s.

4. Compare your results in part with the speed of light.

The grading rubric below is modified from the standard rubric and will be used for this take-home lab report.

Sections

A (90-100%)

B (80-90%)

C (70-80%)

D/F (0-70%)

1. Overall Presentation & Organization

10%

Clear and concise organization, formatting, and language.

Minor organizational problems. Text is unedited.

Several organizational issues. Text is in rough draft form.

Major problems with organization.

2. Introduction

10%

1-3 sentences summarizing the main goals and how they are obtained by experimentation.

Not concise. Goals unclear.

Poor understanding of the goals. Generic statements.

Cursory or missing introduction. Copied from Manual

3. Data

Calculations

Fitting

30%

Clear, concise equations and calculations. Care taken with units. Averages and standard deviation from the mean reported as necessary.

All essential data displayed in graphical or tabular format. No excessive data given. All axes labeled with units included.

Graphs fit with appropriate functions (lines or curves) with fitting parameters reported.

Calculations mostly correct.

Excessive detail or repetition of similar calculations. Excessive raw data included.

One of items at left poorly labeled or missing.

Major calculations missing or clearly needs improved organization.

Some essential data missing or plotted incorrectly.

More than one fit or equation missing.

No calculations given. Data reported without showing work.

Major issues with data presentation.

No fitting done.

4. Questions

30%

Correct and complete answers to all questions in lab manual.

Mostly correct and complete answers to questions.

Incomplete answers or several wrong answers.

Mostly incorrect or missing answers.

5. Results and Discussion

20%

Summary of conclusions drawn with references to values obtained.

Where appropriate, discussion of:

1) actual vs expected results

2) fitting results

3) reproducibility

4) effects from sources of error/precautions

Conclusion not comprehensive. Missing one of the items at left.

Only cursory summarization.

Conclusion inappropriate or missing.

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