Lab02_StandingWave_ConnorEdwards

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Binghamton University *

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152

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Physics

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Apr 3, 2024

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docx

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Standing Wave on a String Connor Edwards PHY-152 Abstract The motion of a standing wave is one of almost an illusionary nature due to how it behaves to the naked eye. At the right frequency, a standing wave looks superimposed over itself as it vibrates back and forth, especially when dealing with string motion. Therefore, it is not only scientifically interesting but also visually appealing to those with no knowledge of the subject. In this experiment, we perform that exact motion with a string to verify whether the given equations are valid representations or not. To do this we attach a hanging weight to the string at one end and oscillate it with a generator at the other to create a standing wave. By increasing the weight and adjusting the generator’s frequency we are able to record the data and calculate our own gravitational constant being 9.13 m/s^2 and compare it to the known constant of 9.81 m/s^2 to evaluate the differences and sources of error in the design. Introduction Standing waves, also known as stationary waves, are the result of two waves moving in opposite directions with equal frequency and amplitude. They effectively cancel each other out due to their opposing forces, which causes them to create a fixed area of oscillating waves. The interference created equates to effectively zero energy being created by the system, at least for a string. Also, the resultant amplitude will be equal to the amplitude of the individual forces. Therefore, the product will be one like the experiment shown here no matter the specific energy put into the system. Experimental Setup To properly begin this lab, one must first get all the materials together including the high function generator which drives the entire lab by providing the oscillation of the string. Then, measure, weigh, and find the density of a 2-meter-long string to record data (fig. 1) by attaching it to the generator and adding mass while slowly increasing the frequency until observing the number of loops. Repeat this step similarly while adding more mass by 50 grams each trial and record in a new data table (fig. 2), converting to kilograms. Process the data into an excel table, and then calculate the percent error for the calculated gravity and the given gravity. Fixed Data Ls= c m Total string length L= c m String length between pulley and wave driver ms = g Total string mass mh = 5 0 g Mass of mass hanger Fig. 1 Trial m [kg] f [Hz] f [Hz] ^2 1 250 --- --- 2 300 --- --- ~~~ ~~~ ~~~ ~~~ 10 700 --- --- Fig. 2
The picture shows the ideal wave motion for the lab, being the third harmonic at a stable frequency to create 3 oscillating sections of string. This picture shows what would be seen on the frequency generator during the in-person lab demonstration as the value for frequency for the third harmonic in Hz. Experimental Data Fixed Data Ls= 225 c Total string length
m L= 160. 5 c m String length between pulley and wave driver ms = 370 g Total string mass mh = 50 g Mass of mass hanger Table used from Fig. 4 of the handout to record the values measured with a meter stick and digital scale in the second demonstration video. Trial m [g] f [Hz] 1 250 36.1 2 300 39.7 3 350 43 4 400 46 5 450 49 6 500 51.6 7 550 54.1 8 600 56.7 9 650 58.9 10 700 61.3 Table for raw measurements before any conversions or calculations that were taken during the testing trials in the third and fourth demonstration videos. Analysis Calculations: -μ = m/L so 370g/225cm or .37kg/2.25m = 0.164 kg/m -f & f^2 = f(3)/3 & f(3) squared respectively so, Trial 1 is 36.1/3 = 12.03 or 12 & 36.1 squared is 1303.2 Repeat for Trials 1-10 -f^2=(g/4*L^2*μ) *m reorganize to find g= (f^2/m)*4L^2*μ This gave the answer 9.13 m/s^2. -Percent error = (measured-accepted/accepted) x100 so, (9.81-9.13/9.81) x100 = 7% error
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