The diagram below shows a wave pulse at \(t = 0\) moving to the right on a string with wave speed \(2 \mathrm{~mm/s}\text{.}\) Each grid box represents \(1 \mathrm{~mm}\text{.}\) Consider two different scenarios:
In Scenario 1 the black dot represents a fixed end for the string
For each scenario: Sketch the shape of the spring at \(t_1 = 2 \mathrm{~s}\text{,}\)\(t_2 = 2.5 \mathrm{~s}\text{,}\) and \(t_3 = 3 \mathrm{~s}\text{.}\) Explain how you made your sketches and comment on the similarities and differences between the scenarios.
Two speakers set to produce in-phase sound waves are located somewhere within the gray circle in the figure below. Using a microphone, you walk around a large circle, marking all positions where the detected sound volume is maximal with a dot and all positions where the detected sound volume is zero with a square. Are the two speakers separated horizontally or vertically? How far apart are they (in terms of the wavelength)?
Two speakers separated by \(10 \mathrm{~m}\) are simultaneously creating identical (with the same initial phase) sound waves with wavelength \(8 \mathrm{~m}\text{.}\) You are standing in between the two speakers (on a line from one speaker to the other) but you do not hear any sound! Determine where you are standing, measured from the center point between the two speakers.
You have now encountered the idea of superposition (the idea of adding together like quantities) in multiple contexts, including Waves and Vectors. Consider your experiences with superposition in these two contexts and write a short reflection about what is similar and different about superposition for waves and for vectors.
