Question

Please answer WARM-UP Questions #1-6.

PROBLEM #2: STANDING WAVE PATTERNS While talking to a friend on the phone you play with the telephone cord. As you shake the cord, you notice the ends of the cord are stationary whi vibrates back and forth; you have a standing wave. As you change the motion of your hand, a new pattern develops in which the middle of the cord is stationary while the rest of the cord vibrates wildly. You decide to investigate these standing wave patterns le the middle of the cord Instructions: Before lab, read the laboratory in its entirety as well as the required reading in the textbook. In your lab notebook, respond to the warm up questions and derive a specific prediction for the outcome of the lab. During lab, compare your warm up responses and prediction in your group. Then, work through the exploration, measurement, analysis, and conclusion sections in sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to perform data analysis, rather than doing it by hand Read SK Chapter 21 EQUIPMENT This problem is done using a tightly coiled metal spring approximately 2 meters in length. Do not stretch the tightly coiled spring past its elastic limit of 8 meters! You also have a meterstick. Hold the stretched spring tightly. Releasing the spring when it is stretched can cause pain and injury to your partner. Safety goggles must be worn to protect your eyes in the event of an accidental release of one end of a stretched spring. Gloves should be worn to protect your hands. WARNING: Never release one end of a spring that is under tension. Doing so might create a snapping motion that could injure somebody. Always release the tension slowly. Wear safety goggles while in the vicinity of the springs. Wear a glove on the hand holding the spring If equipment is missing or broken, submit a problem report by sending an email to [email protected]. Include the room number and brief description of the roblem. WARM UP 1. Draw a sketch of the experimental set-up. On this sketch label the directly 2. From your sketch, determine the boundary conditions for the standing wave. Can 3. Draw sketches of the three simplest standing wave patterns that are consistent with measurable quantities and the unknown quantities the ends of the spring move? your boundary conditions. On your sketch, label the wavelength of each standing wave pattern and the length of the spring 4. Examine your sketch for the simplest standing wave. The frequency of this wave is defined as the first harmonic. From your sketch, find an equation relating the wavelength of the standing wave to the length of the spring. 5. Examine your sketches for the other standing waves. The frequencies of these waves are called the 2nd and 3rd harmonics. Using your sketches, find the equations relating wavelength of the standing wave pattern to the length of the spring for each harmonic. 6. Do you see a pattern in your three equations? For an arbitrary standing wave pattern, or nth harmonic, find an equation expressing the wavelength of the standing wave as a function of n and the length of the spring.

Answer 1

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