A mass of 80 g was hung from the string and three different harmonics were generated in the string. This is shown below in the Setup column (the string is red). The frequency of each harmonic and the frequency uncertainty () has been given. You can determine the harmonic by counting the lobes. To determine wavelength of each harmonic, you must use the blue 4-meter stick provided. The zero end of the 4- meter stick has been exactly lined up with the left end of the string. For the wavelength uncertainty, this is your estimation of how much your measurement of the wavelength could be off by. Last, determine the wave speed and its uncertainty. The formula for the wave speed uncertainty is below (a, is the wave speed uncertainty, o, is the frequency uncertainty, & a; is the wavelength uncertainty). amaitta

Problem: As often noted in lecture, a simple harmonic without particular boundary conditions is highly unphysical - it extends into infinity in space. However, in Lecture 4, we have come to realise how sinusoidal standing waves serve as components in the Fourier series for more complex solutions to the wave equation. In this Discussion, we will examine the wave packet, a construction of a physical wave with finite spatial range. (a) First, to capture the full generality of the wave equation solutions, find the complex right-moving simple harmonic wave. (b) We assert k = . Then, a general wave packet u(x, t) can be constructed as the sum across all possible k values of the right-moving simple harmonic wave, each with amplitude coefficients A(k). What is the form of u(x, t)? Note that we do not have the boundary conditions that would produce standing waves. (c) A(k) is found such that u(x, 0) does not stretch indefinitely in space. What is then an expression for A(k) in terms of u(x, 0)?…

Answer all these questions

Consider the following hypothetical results for an experiment similar to the one you designed and conducted this past week. Refer to Part 2 of the Student Lab Guide, (page 34 on propagation of uncertainty, and pages 53-56 on statistical significance of your results) for assistance. Ben and Jerry tested the dependence of the acceleration of a cart on the net force applied to that cart (a=F/m). The cart mass was known to be 0.600 kg with negligible uncertainty. They plotted acceleration versus force and found the slope of their graph to be 1.70 +/- 0.02. Answer the following questions: (a) What are the units of their slope? Why? (b) What is the expected value of their slope? Why? (c) Is their experimental result consistent with this expected value? Why or why not?