We continue to explore the waves in 1D. We are now looking at the superposition of the sinusoidal waves. We want to look at the superposition of two identical waves moving in opposite directions. The goal for this activity is to figure out the correct conditions for creation of so-called standing waves which is the result of superposition of two oppositely travelling sinusoidal waves. The way we can achieve the superposition of two waves going in opposite directions is to generate a sinusoidal wave with small amplitude and to terminate one end of it with a fixed end clamp

. Explain how clamping the end of string will achieve the effect of having two waves moving in the opposite direction? . The other thing we'll need to do to form a standing wave is to reduce the amplitude of the driver to about 0.1cm (or smaller). Explain why we need to do that. . Look at the simulation and figure out the speed of the wave with no damping and medium tension. To make the measurement easier use the triangular pulse like we did a couple of lectures ago. Explain why we can use triangular pulse shape to measure the speed of the pulse although we are interested in the sinusoidal wave. Report your wave speed with an estimation of uncertainty with your answer. Switch to \"Oscillate\" mode to get back to the sinusoidal waves. . What should the wavelength of your standing wave be in order to create a standing wave with 3 nodes (2 on the ends and one in the middle aka the second harmonic)? Avoid simply looking up the formula but instead support your idea with a clear sketch of the situation at hand and explain how the length of the clamped string is related to the desired wavelength of your standing wave. . Using your results from parts B and C calculate the frequency (with an estimate of uncertainty) of the wave which will guarantee the formation of the second harmonic (3 total nodes). Verify your result with the simulation. The natural harmonics of an object are often referred to as the resonance frequencies of that object (the string in our case). Explain how what you know about resonance from the previous lectures helps you verify your answer. . Change the \"resonance\" frequency by 10% (or by several standard errors of the mean of your answer) and check what happens. Is it still a standing wave? Would you consider that to be a resonance frequency? Explain why. HINT: Make sure to observe your system long enough to see long-time behavior. G. Is there another way to create two sinusoidal waves travelling in opposite directions? Explain. H. With the implementation of the standing wave you identied in part G, what is the frequency at which a standing wave with 3 nodes forms? Calculate that frequency (with an uncertainty) and verify with your simulation. Just like before, check that stepping away from the resonance frequency produces expected results. 1. Combine all of your ndings together and write down formulas for the resonance frequencies of the closed ends string (from part A) and open-closed string (from part G). What are the similarities and what are the differences. Explain. Make sure to provide a good qualitative explanation for your answer and support it with sketches and graphs as necessary. J. BONUS: Write down equation(s) for the resonance frequencies for the string opened on both ends. Make sure to provide a good qualitative explanation for your answer and support it with sketches and graphs as necessary. Explain why our simulation is not useful to reproduce these kinds of standing waves and give an example of an object where these kinds of standing waves can be produced