Two-Source Interference and Beats PHYS 222 Post Lab 5 B. 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 Q and R 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.Lab 4: Two-source Interference and Beats Name: Post Lab: The geometry of two-source 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 diagram 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. Source A Source B . . . .. BP TAP 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 crests (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 further equally spaced wave crests along each line. 2. Now add the position of wave troughs along each line, using a different color. 3. Is point P on a wave crest or in a wave trough with regards to the sound wave emitted by A? 4. Is point P on a wave crest or in a wave trough with regards to the sound wave emitted by B? 5. Is the point P therefore a point of constructive or destructive interference, or somewhere in between? 6. How would your picture change if we "waited" half a wave period? Would your answer to part 5 above still hold?Two-Source Interference and Beats PHYS 222 Post Lab 5 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 P (not necessarily the same point P as above). In the table below the distance from each source to point P is given as a multiple of the wavelength. Assume we "freeze" the wave at 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 interference at P is constructive or destructive. (The last two are tricky!) 'AP A: crest/trough B: crest/trough Interference 42 42 crest crest constructive 42 62 42 4.5 2 62 3.52 7.5 2 9.52 5.82 6.3 2 62 6.25 2 2. Write down a general rule (in words) that allows you to figure out whether the interference at a point is constructive, destructive, or something in between. Your statement should include the phrases "difference in path length", "integer number of wavelengths" and "half-integer number of wavelength". 3. Now express your rule as equations in terms of rAP, /BP, 2 and n, where n is considered an arbitrary integer: "The interference at point P is ... ... maximally constructive if: fully destructive if