1.
How does the shape of the circular wave change as time moves forward? What happens to each crest? Are there any especially interesting moments in time? Explain your reasoning.
Section 7.12 Summary and Extension: 2D Interference
Exercises Activities
Not all waves are one-dimensional—in fact, most waves are two- or even three-dimensional. The diagram below shows a periodic circular wave, where each circle represents a wave crest.
The diagram below shows two overlapping periodic circular waves, their sources separated by some known distance.
2. Explore Path-length Difference.
Suppose that two sources of circular waves are separated by a distance \(d\text{.}\) You are allowed to stand anywhere you want. Wherever you are standing, you measure the distance from you to each of the two wave sources. Then, you subtract these two distances to find the path length difference (\(\Delta D\)). What are the (1) largest and (2) smallest values of the path length difference for this situation? Where are you standing in each case?
Answer.
The largest path length difference is equal to \(d\text{,}\) and you are standing along the line that passes through both sources (not between the sources). The smallest path length difference is equal to 0, and you are standing on the line that passes perpendicularly through the midpoint between the sources.
