Post Lab: The geometry of two-pearce interference In this post lab activity you will explore in more details on how to identify whether an area somewhere in front of the speakers is an area of constructive interference of destructive interference. A. Consider the diagramm below showing the two sources and a point Labeled P in front of them. We want To figure out if the waves interfere constructively or destructively (or something in between) at P. FAP P The two sources A and B are emitting wave crests at the very instant this "picture" was taken. You can also see the previous three wave crews (in red) Of course, the waves really spread out in all directions as you saw in the simulation, but we're only interested in the "part" of the wave that travels towards the point P. 1. Add forther equally spaced wave creus along each ling. 2. Now add the position of wave troughs along each line, esing a different color. 3. Is point P on a wave crest of in a wave trough with regards to the sound wave emitted by AT 4. Is point Pon a wave crest or in a wave trough with regards to the sound wave emined by B? 5. Is the point A therefore a point of countructive or demuchive interference, or somewhere in between . How would your picture change if we "wanted" half a wave period? Would your answer to part 5 above still hold?D. In the picture below you once again see the two sources. They are now placed exactly eight wavelengths apart, as indicated by the scale between the sources (the space between two adjacent markings is one wavelength). Source A Source B R Proceeding as you did in part A above, figure out for points @ and & whether they are points of maximum (or near-maximum) constructive interference, points of destructive interference, or somewhere in between. Use the space below for your calculations,C. Now let's generalize your results. 1, Think about some examples to establish a pattern. Call the sources 'A" and 'B' as before, and refer to the point as point I (not necessarily the same point Pas above). In the table below the distance from each source to point P is given as a multiple of the wavelength. Assome we "freeze" the wave m a time when the sources are emitting a wave crest. For each example enter whether the wave from source A has a crest or trough at point P, and whether the wave from source B has a crest or trough at point P. Then write in the last column whether or not the imerference al P is constructing or destructive. ( The last Iwas are tricky!) As crewwrough B: crest/trough Interference 41 41 crest crest constructive 61 457 151 751 952 632 6.35 1 1. Write down a general rele (in words) that allows you to figure out whether the imerference at a point is constructive, destruction, or something in between. Your sowement should include the phrases "difference in park length", "integer number of wavelengths" and "hay inleger sunher of wavelength". 3, Now express your rule as equations in terms of ran for. & and n, where a is considered an arbivary integer: "The Interference at point Pis .. .. normally carnnow if: -. fully destructive in