Exp. #1-9 : Measurement of the Characteristics of the Wave Interference by Using a Ripple Tank

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1 PAGE 1/18 Exp. #1-9 : Measurement of the Characteristics of the Wave Interference by Using a Ripple Tank Student ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time Submission Place Introductory Physics Office Report Box # Students should write down Student s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding contents to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor. Instead, it is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the time specified by Experiment Lecturers. The Experiment Report score per each Experiment Class is evaluated by max. 50 points (basically 15 points). Solutions of Problems in Experiment Reports are not announced to the public according to the General Physics Laboratory - Administration Rule. If a student permits other students to pirate one s Experiment Reports or a student pirates Experiment Reports of other students regardless of permission of original creators, the corresponding Experiment Report score and Active Participation score will be zero in case of exposure of such situation. Unless Experiment Reports are submitted to the place due to the time specified by Experiment Lecturers, the corresponding Experiment Report score will be zero. If the submission rate of Experiment Reports is less than or equal to two thirds, the grade of General Physics Laboratory will be F level. In order to decide grades of General Physics Laboratory at the end of current semester, the detailed scores of General Physics Laboratory will be announced at Introductory Physics Office homepage. Based on the announcement, students can raise opposition of score error. Since the public evidence is needed for the confirmation of opposition, students should keep one s Experiment Reports completed evaluation by Experiment Lecturers until the Experiment Report score decision If a student is absent from the Experiment Class because of proper causes, the corresponding student should submit documents related to absence causes to Introductory Physics Office regardless of cause occurrence time until the grade decision of General Physics Laboratory. If a student moves the Experiment Class arbitrarily without permission of Introductory Physics Office, it is noted that the total Experiment Scores will be zero. Lecturer's Mentioned Items Submission Time/Place Check Experiment Report Score Evaluation Completion Sign 50

2 PAGE 2/18 1. Objective Student ID Name The wave interference pattern due to two wave sources in a ripple tank will be observed, and the wavelength and the speed will be evaluated from the observed patterns. 2. Theory (1) Conditions for a perfectly constructive interference and a perfectly destructive interference If two waves with equal amplitude, equal frequency, and equal phase with a path difference have an oscillation displacement as sin and sin respectively, the resultant wave due to the superposition of two waves is given as follows: cos sin (Eq. 1) Here, is called the wave number or the propagation constant having the relation with the wavelength. The condition for the perfectly constructive interference when the resultant wave has the maximum amplitude is given as follows: cos ±,, (Eq. 2) Here, is an integer. If the path difference between two waves is an even number times half the wavelength, a perfectly constructive interference can be observed. The condition for the perfectly destructive interference when the resultant wave has the minimum amplitude is given as follows: cos,, (Eq. 3) Here, is an integer. If the path difference between two waves is an odd number times half the wavelength, a perfectly destructive interference can be observed. For the case of two waves with equal amplitude, equal frequency, and opposite phase, note that the conditions for the perfectly constructive interference and the perfectly destructive interference described by (Eq. 2) and (Eq. 3) are interchanged with each other. (2) Approximate formula for the path difference Assume that two waves with equal wavelength and equal phase produced at two wave sources and displaced by the distance from each other are interfered as shown in Fig. 1. Introducing an arbitrary screen displaced by the distance from the midpoint of two wave sources and parallel to the line connecting two wave sources, the path difference at the point displaced by the distance from the center of the screen is given as follows: sin (Eq. 4) Fig. 1. Approximate formula for the path difference when considering wave interference. (The solid lines and the dashed lines connect the points of the perfectly constructive interference and the perfectly destructive interference, respectively.) Here, is the angle between two lines which start at the midpoint of two wave sources and pass through the center and point on the screen, respectively. (Eq. 4) is the approximate formula for. If the point on the screen is in a perfectly constructive interference, the wavelength and the speed are given as follows: sin,, (Eq. 5) (Eq. 6)

3 PAGE 3/18 On the contrary, if the point on the screen is in a perfectly destructive interference, the wavelength and the speed are given as follows: sin,, (Eq. 7) (Eq. 8) Answer the following questions. 1. Referring to Young s experiment involved in the optical interference, show the procedure obtaining (Eq. 4).

PAGE 4/18 3. Experimental Instruments Items Quantity Usage Clean up method Ripple tank 1 set After water is poured into the ripple tank, the wave interference pattern is observed.

4 PAGE 4/18 3. Experimental Instruments Items Quantity Usage Clean up method Ripple tank 1 set After water is poured into the ripple tank, the wave interference pattern is observed. It should be placed at the center of the experiment table. Light source 1 ea. It is used to provide Strobe or Steady mode. It should be attached to the ripple tank. Ripple generator 1 ea. It is used to control the operation of two wave sources and a light source. It should be attached to the stand. Projection screen 1 ea. It is used to sketch the wave interference pattern. It should be attached to the ripple tank. Mirror 1 ea. It is used to reflect the wave interference pattern to the projection screen. It should be attached to the ripple tank. Stand 1 ea. It is used to support the ripple generator. It should be placed at the center of the experiment table. Beaker 1 ea. It is used to pour water into the ripple tank and remove water inside the ripple tank. It should be placed inside the basket of the experiment table. Power adaptor 1 ea. It is used to connect the ripple generator to the wall power. It should be placed inside the basket of the experiment table. Paper for sketching & Scale 1 set It is used to sketch and analyze the wave interference pattern. It should be placed inside the basket of the experiment table. Paper towel 1 ea. It is used to remove water. It should be placed inside the basket of the common experiment table.

ripple generator to the wall power and keep the ripple generator off. Connect the light source to the ripple generator.

1) Select Strobe mode of the light source and turn on the light source.

5 PAGE 5/18 4. Experimental Procedures (0) Setting before the experiment (1) Observation of a wave interference pattern in Strobe mode 1) Use the ripple generator-to-power adaptor & connection cable to connect the ripple generator to the wall power and keep the ripple generator off. Connect the light source to the ripple generator. In order to prevent an electricity accident, note that the electric parts of the experimental instruments must not be in contact with water. 1) Select Strobe mode of the light source and turn on the light source. 2) After tightening the valve of a water drain tube, pour water into the ripple tank with a beaker and remove remained water inside the beaker. 2) Set the phase of the ripple generator to in phase. Control the frequency and the amplitude of the ripple generator properly and sketch the wave interference pattern displayed in the projection screen on the paper by indicating bright arcs. 3) Control the horizontal state of the ripple generator by rotating dipper adjust knobs of the ripple generator. Place the wave source in contact with the surface of water. 3) Set the phase of the ripple generator to out of phase and sketch the wave interference pattern in the same manner. 4) Analyse the wave interference pattern obtained in Strobe mode by using the following steps. 4) After confirming that the light source is off and the amplitude of the ripple generator is zero, turn on the ripple generator. a) Measure the actual distance and the distance on the paper for sketching between two wave sources and by using a scale and calculate the ratio.

PAGE 6/18 b) Draw the arbitrary screen displaced by a certain distance from the midpoint of two wave sources and parallel to the line connecting two wave sources.

6 PAGE 6/18 b) Draw the arbitrary screen displaced by a certain distance from the midpoint of two wave sources and parallel to the line connecting two wave sources. 3) Set the phase of the ripple generator to out of phase and sketch the wave interference pattern in the same manner. c) Draw the lines connecting the points in a perfectly constructive interference from the intersections of bright arcs. 4) Analyse the wave interference pattern obtained in Steady mode by using the following steps. Answer the following questions. 2. Water surface acts as a lens so that the ridge positions in Strobe mode appears as bright arcs. If the frequency is, explain how bright arcs in Strobe mode changes as the frequency of light source changes from to. a) Measure the actual distance and the distance on the paper for sketching between two wave sources and by using a scale and calculate the ratio. b) Draw the arbitrary screen displaced by a certain distance from the midpoint of two wave sources and parallel to the line connecting two wave sources. d) After finding the points in a perfectly constructive interference on the screen, write down the integer corresponding to a perfectly constructive interference. e) Case of in phase : Calculate the wavelength on the paper for sketching from the exact formula. By using the ratio, evaluate c) After finding the points in a perfectly destructive interference on the screen, write down the integer corresponding to a perfectly destructive interference. d) Case of in phase : Calculate the wavelength on the paper for sketching from the exact formula. By using the ratio, evaluate the wavelength and the speed. the wavelength and the speed. e) Case of out of phase : Calculate the wavelength on the paper for sketching f) Case of out of phase : Calculate the wavelength on the paper for sketching from the exact formula. By using the ratio, evaluate the wavelength and the speed. (2) Observation of a wave interference pattern in Steady mode 1) Select Steady mode of the light source. 2) Set the phase of the ripple generator to in phase. Control the frequency and the amplitude of the ripple generator properly and sketch the wave interference pattern displayed in the projection screen on the paper by indicating destructive interference lines. from the exact formula. By using the ratio, evaluate the wavelength and the speed. f) Predict the theoretical number of destructive interference lines from the distance between two wave sources and the wavelength, and compare it with the experimental number of destructive interference lines on the paper for sketching. 5) If the measurement is finished, turn off the light source and control the amplitude of the ripple generator to zero so as to turn off the ripple generator. After placing the beaker at the end of a water drain tube, loosen the valve of a water drain tube and remove water inside the ripple tank. Clean up the experimental instruments according to the suggested method.

7 PAGE 7/18 5. Experimental Values (1) Observation interference pattern in Strobe mode 1) Case of in phase Distance between two wave sources Formula: Exact wavelength on the paper for sketching Frequency (Hz) Distance between two wave sources Distance on the paper for sketching Path Integer Even number difference Exact wavelength Wavelength Speed (cms) Average Average Average

8 PAGE 8/18 Frequency (Hz) Phase In phase Mode Strobe After analyzing the wave interference pattern, attach the paper for sketching here.

9 PAGE 9/18 Frequency (Hz) Phase In phase Mode Strobe After analyzing the wave interference pattern, attach the paper for sketching here.

10 PAGE 10/18 Frequency (Hz) Phase In phase Mode Strobe After analyzing the wave interference pattern, attach the paper for sketching here.

11 PAGE 11/18 2) Case of out of phase Distance between two wave sources Formula: Exact wavelength on the paper for sketching Frequency (Hz) Distance between two wave sources Distance on the paper for sketching Path Integer Odd number difference Exact wavelength Wavelength Speed (cms) Average

12 PAGE 12/18 Frequency (Hz) Phase Out of phase Mode Strobe After analyzing the wave interference pattern, attach the paper for sketching here.

13 PAGE 13/18 (2) Observation interference pattern in Steady mode 1) Case of in phase Distance between two wave sources Formula: Exact wavelength on the paper for sketching Frequency (Hz) Distance between two wave sources Distance on the paper for sketching Path Integer Odd number difference Exact wavelength Wavelength Speed (cms) Average Predict the theoretical number of the destructive interference lines from the distance between two wave sources and the wavelength. # of the destructive interference lines Theoretical value Experimental value

14 PAGE 14/18 Frequency (Hz) Phase In phase Mode Steady After analyzing the wave interference pattern, attach the paper for sketching here.

15 PAGE 15/18 2) Case of out of phase Distance between two wave sources Formula: Exact wavelength on the paper for sketching Frequency (Hz) Distance between two wave sources Distance on the paper for sketching Path Integer Even number difference Exact wavelength Wavelength Speed (cms) Average Predict the theoretical number of the destructive interference lines from the distance between two wave sources and the wavelength. # of the destructive interference lines Theoretical value Experimental value

16 PAGE 16/18 Frequency (Hz) Phase Out of phase Mode Steady After analyzing the wave interference pattern, attach the paper for sketching here.

17 PAGE 17/18 6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) Write down contents in terms of the following key points. 1. Explain the change of wavelength and speed due to the frequency. (Suggest why the speed is constant.) 2. Compare the constructive and destructive interference points between the Strobe and Steady modes or the cases of in phase and out of phase. 3. In the case of the physical quantity without the theoretical value such as the speed, investigate the procedure using the report value with the form of [ average ] ± [ multiple of standard deviation ]. (Explain the procedure determining the multiple of standard deviation, relating with the normal distribution curve and the confidence level.)

18 PAGE 18/18 7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) 8. Reference

General Physics Laboratory Experiment Report 2nd Semester, Year 2018

General Physics Laboratory Experiment Report 2nd Semester, Year 2018 PAGE 1/13 Exp. #2-7 : Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface Measurement of the Light Wavelength and the Index of Refraction of the