Lab 9 _ Waves and Resonance (1)

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Louisiana State University *

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Jan 9, 2024

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Lab 9: Waves and Resonance Purpose: The purpose of this lab is to further understand the concept of waves, resonance, oscillations, and frequencies. Procedure: For this lab, we attached a string to a support rod at one end and laid the other side through a pulley. We then added a hooked mass of 200g to the hanger pan. Using the function generator to find the amplitude and frequency for the first harmonics to appear. After the first harmonic is found, we continue to adjust the function and generator until n =2,3,4, and 5. Finally, we added 200g more to the mass hanger pan and repeated the previous steps. Analysis : 1. Tension (1)= mass * gravity = (0.2494kg)(9.8m/s^2) = 2.44N a. Tension (2)= mass * gravity = (0.4494kg)(9.8m/s^2) = 4.40N 2. Mass density = Total mass/ measured length = (0.00150kg)/(1.442m) = 0.00104kg/m 3. Mass density = Tension/(wave speed^2) = 2.44/(47.47^2) = 0.00108kg/m 4. Percent error = (theoretical - experimental)/ theoretical = (0.00104-0.00108)/0.00104 *100 = 3.84% 5. Mass density = Total mass/measured length = 0.00104kg/m a. Mass density = 4.40/(66.68^2) = 0.0009896kg/m b. Percent error = (theoretical - experimental)/ theoretical = (0.00104- 0.0009896)/0.00104 = 4.9% Reflection: 1. The smallest point we can measure on the meter stick is a millimeter which is 0.0005 m of uncertainty. No, the instrument uncertainty is not equal to the uncertainty of the frequency because the instrument uncertainty is increased because there is also human error when reading the instruments. 2. The triple beam balance will have some uncertainty because it is not exact. The string that we used, we measured the points that we needed for the wavelength, but we needed the total length of the string for the mass density. Also, we did not check the string for any knots which also could have increased the mass of the string in certain points. 3. According to my percent error the mass densities are very similar with only a 3.84% percent error so both ways are valid for calculating mass density. 4. The string was not completely inextensible due to the hanging or added length of it holding the mass pass and the weights as well as it being connected at a point on the inside of the string instead of at the tip leaving our numbers in our calculations on both mass densities smaller than expected 5. This happened because the resonance was causing the string to make the mechanic clip bounce back and forth. The clip bouncing in the cylinder basically matched the natural frequency and caused vibrator to also match the natural frequency which is why it started to shake. Application:

1. Wavelength= 2L/n = (2 * 8)/12 = 133.33 cm 2. The frequency that is produced in a wire is proportional to the square of the resonating length of the wire. When different keys are pressed on the piano, the vibrating length is what is being changed. The vibrating length of the string present inside it over which different frequencies are produced without the need of having different lengths of the wires. Analysis: In the packet Data Tables: In the packet Conclusion: In conclusion, this lab allowed me to further understand the concept of waves, resonance, oscillations, and frequencies.

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