Topic: H 5 HW2.pc C Numeric Grades PHYS& 0 1/1 1 5 PHY X * Homew Course PHYS 2 Grades Week 3 = applica Log In t + X C @ File | /home/chronos/u-a3a8fc65d25da15ca30eaf6d460148defb16463e/MyFiles/Downloads/PHYS%20223%20Lab2_online.pdf E PHY 203 1 / 3 100% Abstract The frequency of a string vibrator will be calculated by studying the standing wave patterns in a string. The wave speed in a spring will also be measured. This is a short simple lab given I had little time to create it since we suddenly moved online. Introduction A wave is a propagation of a disturbance or energy. When a stretched string is disturbed, the wave travels along the string. Upon reaching the fixed end of the string, the wave is reflected back along the string. The propagating waves interfere with the reflected waves and the superposition of the waves can result in a standing wave pattern under certain conditions-when the frequency of the oscillator matches the natural frequency of the fixed string, resonance occurs and the string vibrates with a large amplitude. But unlike a mass on a spring, there are multiple natural frequencies for this system. You will study standing waves in this lab The velocity of the wave in the string is given by V= and V= Af Where 7 is the tension in the string, u is the mass per unit length of the string, 2. is the wavelength of the wave and f is the frequency of the wave (in cycles per second or Hertz). Note: T is tension (in Newtons), not period! Standing Waves in a String Methods Since this lab is online, I will provide you data that you will analyze. I will show you video of the equipment set up and what was measured during the explanation of the lab at the start of the lab period on Zoom. From the equations above, if you want to figure out the frequency of the oscillator you should see you will need to know the speed of the wave and the wavelength. To get the speed of the wave you will need the Tension in the string and u, the mass per unit length of the string. An 0.845 m long piece of string has a mass of 0.81 grams. Calculate u: String is tied to the end of a Pasco string vibrator and then passed over a pulley a distance L away. L was measured to be 1.992 m. The figure below shows a mass hanging from a pulley (to minimize friction forces). The hanging massTopic: H 5 HW2.pc C Numeric Grades PHYS& 0 1/1 1 5 PHY X * Homew Course PHYS 2 Grades Week 3 = applica & Log In t + X C @ File | /home/chronos/u-a3a8fc65d25da15ca30eaf6d460148defb16463e/MyFiles/Downloads/PHYS%20223%20Lab2_online.pdf E PHY 203 1 / 3 100% + Standing Waves in a String Methods Since this lab is online, I will provide you data that you will analyze. I will show you video of the equipment set up and what was measured during the explanation of the lab at the start of the lab period on Zoom. From the equations above, if you want to figure out the frequency of the oscillator you should see you will need to know the speed of the wave and the wavelength. To get the speed of the wave you will need the Tension in the string and u, the mass per unit length of the string. An 0.845 m long piece of string has a mass of 0.81 grams. Calculate u: String is tied to the end of a Pasco string vibrator and then passed over a pulley a distance L away. L was measured to be 1.992 m. The figure below shows a mass hanging from a pulley (to minimize friction forces). The hanging mass provides the tension T in the spring. The string vibrator moves up and down rapidly and waves travel to the left down the string, bounce off of the end with the pulley and travel back toward the vibrator. If the tension is just right, standing waves are formed. The picture shows a standing wave pattern that is two wavelengths long. There are 5 nodes where the string doesn't move (ok, it moves a little at the vibrator) and 4 antinodes where the string moves up and down a lot. String String vibrator Hanging massTopic: H 5 HW2.pc C Numeric Grades PHYS& 0 1/1 1 5 PHY X * Homew Course PHYS 2 Grades Week 3 = applica & Log In t + X C @ File | /home/chronos/u-a38fc65d25da15ca30eaf6d46b148defb16463e/MyFiles/Downloads/PHYS%20223%20Lab2_online.pdf E PHY 203 2 / 3 100% The actual experiment will consist of starting the vibrator in motion and adding mass to the hanger hanging from the pulley. For most masses you use, the string will vibrate wildly (with amplitude about the same as the amplitude of the vibrator arm). However, when you have precisely the right tension in the string, a whole number of "half-wavelengths" or "loops" will fit into the distance between the vibrator and the pulley (roughly). When this happens, the waves traveling away from the vibrator will be in "resonance" with the waves reflected back from the pulley, and the string will exhibit a standing wave pattern with much greater amplitude. Masses were added to get different standing wave patters with different numbers of antinodes. Here is the data collected that you will use: Number of antinodes Mass in grams 10 47.3 9 58.9 8 77.0 7 102.2 6 141.7 5 207.2 4 334.5 590.0 N O 1310.0 Use the data provided to plot a graph of the speed v of the wave versus the wavelength. You should see a linear relationship. Include all data used (you can use Excel) with your report. Include a graph of this data along with a best fit line and its equation. Make sure the graph takes up at least 1/2 a page and is appropriately labeled. Results Show one sample calculation for the data with 5 antinodes. What is v? What is 2?Topic: H 5 HW2.pc C Numeric Grades PHYS& 0 1/1 1 5 PHY X Homew Course PHYS 2 Grades Week 3 = applica & Log In t + X C @ File | /home/chronos/u-a3a8fc65d25da15ca30eaf6d460148defb16463e/MyFiles/Downloads/PHYS%20223%20Lab2_online.pdf E PHY 203 2/ 3 100% What is A? Draw a sketch of the standing wave pattern for 5 antinodes below, labeling 2 on the sketch: Discussion The number of antinodes (loops) n, an integer, defines what is known as the normal modes. n = 1 is called the fundamental mode (or 15t harmonic); n = 2 is the second harmonic; n = 3 is the third harmonic, etc...Study your data and write a general equation showing how the wavelength 2, L and n are related.Topic: H 5 HW2.pc C Numeri Grades PHYS& 0 1/1 1 5 PHY X * Homew Course PHYS 2 Grades Week 3 = applica & Log In t + X C @ File | /home/chronos/u-a38fc65d25da15ca30eaf6d46b148defb16463e/MyFiles/Downloads/PHYS%20223%20Lab2_online.pdf E PHY 203 3 / 3 100% Discussion The number of antinodes (loops) n, an integer, defines what is known as the normal modes. n = 1 is called the fundamental mode (or 15t harmonic); n = 2 is the second harmonic; n = 3 is the third harmonic, etc..Study your data and write a general equation showing how the wavelength 2, L and n are related. Conclusion What is the physical meaning of the slope of the line of your graph? If you can answer the above question, calculate the % difference from your slope data to the "accepted" value of that quantity