Tech 2520-Waves Lab p2 v3(2) copy

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Apr 3, 2024

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1 TECH 2520 Networking Essentials for Technology Waves Lab, Part 2 Introduction This lab is a continuation of the analysis of periodic composite analog waves from Waves Lab, Part 1. Purpose The purpose of this lab is to: ● Repeat all of the purposes in Waves Lab, Part 1; ● Observe how to approximate triangle, square (periodic digital signal), sawtooth and wavepacket functions from a composite analog signal. We will continue to use a simulation entitled, Fourier: Making Waves , located at http://phet.colorado.edu/en/simulation/fourier . You may investigate other websites for information as you complete this assignment; please insert links as citations. Write all answers in your own words. Notes: - Remove current screenshots and replace them with your own. Your screenshots should be focused on the pertinent lab material, not your entire computer screen. - Please keep the document format intact. 1) Keep the amplitude of A 1 set to 1 and set A 2 to 1 as well. Set Graph Controls to Function of: space (x) and Series: sin. In Measurement Tools , turn on the Wavelength tool ( λ 1 ). Toggle between

2 Wavelength tools λ 1 and λ 2 . Take two screenshots of the harmonics, one showing λ 1 and the other showing λ 2 . Take one screenshot of the sum. You should have 3 screenshots in total. Q1-1) What is the relationship between λ 1 and λ 2 ? Write a simple expression. λ 1 = λ 2. X 2 λ 1 is two times bigger than λ 2 2) Keep the amplitude of A 1 set to 1 and set A 2 to 1. Set Graph Controls to Function of: time (t) and Series: sin. In Measurement Tools , turn on the Period tool (T 1 ). Toggle between Period tools T 1 and

3 T 2 . Take two screenshots of the harmonics, one showing T 1 and the other showing T 2 . Take one screenshot of the sum (set to Auto scale). You should have 3 screenshots in total. Q2-1) Compare parts 1) and 2). What are the differences and similarities? - In part 1 we focused on space while in part 2 was based on time. The similarities of both parts 1 and 2 is that both go down at the same points and have the same amplitudes. Q2-2) What is the relationship between T 1 and T 2 ? Write a simple expression. - T 1 = T 2 x2 - T 1 is 2 times bigger than T 2 Q2-3) What is the relationship between f 1 and f 2 ? Write a simple expression. - F 1 = 1/T 1 = 1/0.00228 = 439 hz - F 2 = 1/T 2 = 1/0.001114 = 877 hz - F 2 is half the size as F 1

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4 3) Investigate the other preset function settings . a) Triangle – insert a screenshot of your result below. Include all plots. Qa-1) What do you observe about the amplitudes A 1 - A 11 ? Compare even and odd harmonics. - In A 1 – A 11 the numbers are going down and they are alternating from positive to negative numbers. The even harmonics are all 0 while the odd harmonics have amplitude. Qa-2) What happens to the Sum plot as you decrease the number of harmonics down to 1? - The sum plot as you decrease the number of harmonics down to 1 becomes more like the harmonics graph

5 Qa-3) What happens to the Sum plot as you then increase the number of harmonics back up to 11? Check the infinite harmonics box and compare the black wave (sum) and the gray wave (infinite harmonics). - What happens to the sum plot as you increase the number of harmonics back up to 11 is that the sum of harmonics 1 with infinite harmonics has a gray line and as you move up to h11 it fills out the gray lines with a black solid line b) Square – insert a screenshot of your result below. Include all plots.

6 Qb-1) What do you observe about the amplitudes A 1 - A 11 ? Compare even and odd harmonics. - According to my observations about the amplitudes A 1 – A 11, the even harmonics are all 0 amplitude while the odd harmonics start high and slowly decrease in amplitude as it goes down the harmonics. Qb-2) What happens to the Sum plot as you decrease the number of harmonics down to 1? - The sum plot becomes more like the harmonics plot as you decrease the number of harmonics down to 1. Qb-3) What happens to the Sum plot as you then increase the number of harmonics back up to 11 ? Check the infinite harmonics box and compare the black wave (sum) and the gray wave (infinite harmonics). - The sum plot on harmonics 1 with infinite harmonics has a gray line and as you increase the number of harmonics back to 11 it becomes more like the shape of the gray line c) Sawtooth – insert a screenshot of your result below. Include all plots.

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7 Qc-1) What do you observe about the amplitudes A 1 - A 11 ? Compare even and odd harmonics. - The amplitude is increasing from A 1 – A 11, The even harmonics are all negative amplitudes while the odd harmonics are all positive Qc-2) What happens to the Sum plot as you decrease the number of harmonics down to 1? - The sum plot becomes more like the harmonics graph as you decrease the number of harmonics down to 1 Qc-3) What happens to the Sum plot as you increase the number of harmonics back up to 11 ? Check the infinite harmonics box and compare the black wave (sum) and the gray wave (infinite harmonics). - The sum on the harmonics 1 with infinite harmonics has a gray line as you increase harmonics back to 11 it becomes more like the shape of the gray line

8 d) Wavepacket – insert a screenshot of your result below. Include all plots. Qd-1) What do you observe about the amplitudes A 1 - A 11 ? - According to my observations, A 6 the amplitude peaks and each side of the amplitude drops by the same amount and in the same numbers. Qd-2) What happens to the amplitudes and Sum plot as you decrease the number of harmonics down to 1? - The amplitudes and sum plot becomes more like the harmonics graph as you decrease the number of harmonics down to 1.

9 Qd-3) What happens to the amplitudes and Sum plot as you increase the number of harmonics back up to 11? - The amplitudes and sum plot is random except for the ones around the center by time 0 the amplitude follows the sum line in just that place because the other lines are more random 4) What changes if you repeat the above steps for (3a-d) but change “ Graph controls ” to space and time (x, t)? In “ Measurement Tools ”, turn on both the Wavelength and Period tools. Generalize for all previous settings. - It stays the same the only thing that changes is the time vs the space 5) Now choose the “Wave Game” tab at the bottom of the simulation. Start with Level 1. Match the pink function by setting appropriate amplitudes in the top plot. The game will open a new window when you have achieved a matched setting. After 3 wins on a level, try the next level. Have fun! How many levels did you get to? Can you find any procedure to determine how to match the pink function, or is it trial and error? - After I got past level 2 I used trial and error although, I went based on how the waves looked as well if the waves looked shorter I knew I needed to use higher amplitude.

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