Experiment 303: Transverse Wave: Frequency of VibrationRaagas, Michelle Mae G. School of Chemical Engineering, Chemistry, Biological Engineering, and Material Science Engineering Mapua Institute of Technology, 658 Muralla St., Intramuros, Manila City, Philippines [email protected] OBJECTIVE: The purpose of this experiment is to analyze the concept of frequency of vibration with respect to the transverse wave. To verify each stretched string’s frequency of vibration is the main goal of this experiment. In addition, it also aims to identify how the tension and linear mass density affects the vibrating string’s frequency. On this experiment, each group is given a specific frequency and the assigned frequency on our group is 96.30 Hz. First thing to do after the set-up of the apparatus is to adjust the amplitude and frequency depending on the assigned frequency given by the professor. It can modify using the two knobs located at the upper right of the sine wave generator. See figure 2. METHODOLOGY: For the objective to be accomplished. The use of equipment is necessary for this experiment. It will help us to collect different sets of data which will be useful to achieve the objectives. Below are the materials used in this experiment. Figure 2. Sine wave generator Figure 1. Materials used for the experiment “transverse wave: frequency of vibration” (string vibrator, sine wave generator, iron stand with clamp, pulley, weights, mass hanger, extension cord, meter stick, and guitar string). The goal of the part 1 of this experiment is to determine the frequency of vibration with constant linear mass density which means that the diameter of the wire is constant and also its linear mass density. To do so, choose the size of the string to be used for this entire part of the experiment, carefully tie the end of the guitar string on the string vibrator and the other end is attached with a mass hanger and is then hanged over a pulley. The next step is to add a certain mass on the mass hanger. Observe the string until it forms Figure 3. increase the mass that is added on the mass hanger every trial. Standing waves . After you gather all the data that is needed.a segment. Figure 5. here in part two. you will use five different strings with different diameter and linear mass density. You can adjust it using the amplitude knob or by adjusting the distance between the two iron stand. Notice if the string has a curve edges because it can cause errors and more difficult to form a standing wave. Figure 4. Curved edges After getting all the data. you are now able to solve the frequency of vibration with variable linear mass density. Adjusting the distance and amplitude until the string forms a standing waves When you see a standing wave (refer to figure 4) measure its length and record it also the number of segment that is formed. you can now solve the frequency of vibration that has a constant linear mass density. You will use the same mass on the mass hanger for every trial. Repeat the said step for five times but this time. See the figure below. The process on the part two of the experiment is the same as the part one but unlike in the part one that you will only use one string. The linear mass density of the string is already given depending on the diameter of the string that is used. 31+81.16 Hz 90.18 − 96.07 93.89 % 96.4% Tension (T) T 𝜇 dynes g/cm 1 0.09 89.81 81.02 0.09 44100 29400 24500 90. .54 89. Frequency of vibration with constant linear mass density Linear mass density 𝑛 40000 Frequency (Hz) Actual value of frequency of vibration: 96.015 0.41 93.81+81.77 Hz 𝛼𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝛼𝑎𝑐𝑡𝑢𝑎𝑙 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 = | | 𝛼𝑎𝑐𝑡𝑢𝑎𝑙 34300 39200 80.16 20000 0 86.0184 Trial Tension.0112 93.16 𝐻𝑧 Average frequency = 96.07+93.29 96. determining the frequency of vibration (constant linear mass density) Diameter of wire: 0.09 Hz 86.16 GRAPH Table 2.89 % 86.020 in 0.31 81.30 Hz 9.017 in 0. Frequency of vibration with variable linear mass density.77 − 96. T n L (mass of pan) x 980 cm/𝑠 2 Frequency of vibration (cm) 𝑓= 1 24500 dynes 1 6 2 29400 dynes 1 7 3 34300 dynes 1 8.0039 39200 2 0.16+90.54+89. Frequency of vibration 0.09+86.010 in 0.07 𝐻𝑧 Average frequency = 88.0184 0.0184 39200 Average frequency of vibration Actual value Percentage error Sample computation Trial diameter Tension vs.09 5 = 89.07 89.0184 = 88.022 in 0.41 93. Linear Mass Density= 0.09 88.0184 = 96.0078 0.0078 39200 3 0.4 % 96.30 Hz Table 1: 60000 Linear mass density vs. Determining the frequency of vibration (variable linear mass density) n L 1 1 1 1 1 18 12 10 9 9 f Hz 88.0112 39200 4 0.DATA and SAMPLE COMPUTATIONS Table 1.0039 0.014 in 0.16 Table 2: 𝑛 𝑇 1 39200 Trial 1: 𝑓 = 2𝐿 √𝜇 = 2(18) √0.18 96.01 5 = 86.41+93.54 0 81.31 Hz 81.16 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 = | | = 7.81 Frequency (Hz) Frequency of vibration Graph 2.16 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 = | | = 9.77 Hz 96. Frequency of vibration 𝑇 1 24500 Trial 1: 𝑓 = 2𝐿 √𝜇 = 2(6) √0.0150 39200 5 0.29+80.5 4 39200 dynes 1 9 5 44100 dynes 1 9 Average frequency of vibration Actual value Percentage error 𝑛 𝑇 √ 2𝐿 𝜇 19.30 7.01 Hz 86.18 Hz 𝛼𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝛼𝑎𝑐𝑡𝑢𝑎𝑙 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 = | | 𝛼𝑎𝑐𝑡𝑢𝑎𝑙 89.01 Frequency of vibration Graph 1.022 in.29 Hz 80. Ricardo De Leon for teaching us the process in this experiment and for being my professor also on my physics lecture that helps me to understand the concept behind the experiment.137 . This time. 2011 [2] King. 9th Edition. CONCLUSION By performing this experiment. F.. In addition. The first one is the effect of tension with constant linear mass density and the second is the reverse of it which is the tension is constant and the linear mass density is the one that is changing. I would like to thank my group mates for the participation and for making this experiment fun and interesting just like when the string is starting to form standing wave we were like ‘whoa great’. it is more difficult for the string to form standing waves if it has some curve edges. we observed that as we add mass to the pan. Thank you so much! Based on the gathered data. It is because we adjusted the distance between the two iron stand until it forms wave. the mass on the pan for each trial and so is the tension. and we also observed that as the diameter of the wire increases. the one that is changing is the diameter of the wire and the linear mass density. the length of the string’s standing wave decreases. Lastly. G. the two objectives of the experiment were obtained by applying the concept of transverse wave and relating it on our experimentation. we used the string that is 0.ANALYSIS OF DATA ACKNOWLEDGMENT On the part 1 of the experiment.022 inches in diameter since one of my groupmates suggested it. the number of segment and the length of it will also change. Also.. I would also like to recognize the effort of the lab assistant who provides us the experiment and for explaining the proper way to handle it. the tension also increases as well as the length of string that forms segment of wave. we are able to determine the string’s frequency of vibration. On the second part of the experiment. As I said earlier. There are factors that can affect the experiment and can cause earlier. By using different kind of string. Fundamentals Of Physics. The second objective of this experiment which is to determine how the linear mass density and the tension can affect the vibrating string’s frequency was attained by performing the two parts of the experiment. One of these are the strings that are used. From the time that we change the tension of the string. p. √ REFERENCES [1] Halliday. I would like to thank my friend for making me a cup of coffee while I was doing this lab report. Vibrations and waves. I therefore conclude that 1 𝑓 ∝ √𝑇 𝑎𝑛𝑑 𝑓 ∝ 𝜇. I would like to thank everyone for helping me in my studies especially God for guiding me. since the diameter and the linear mass density of the wire is constant. I would also like to thank our professor Mr.