two stones are dropped simultaneously into a calm pool of water. The crests of the resulting waves form equally spaced concentric cicles, as shown in the figures. The waves interact with each other to create certain interference patterns.

Question

explain why the red dots lie on an ellipse
explain why the blue dots lie on a hyperbola

Answer 1

The red dots lie on an ellipse because the two stones dropped into the pool of water create two circular waves that interfere with each other. The interference of the two waves creates a pattern of constructive and destructive interference, which results in the red dots forming an ellipse.

The blue dots lie on a hyperbola because the two stones dropped into the pool of water create two circular waves that interfere with each other. The interference of the two waves creates a pattern of constructive and destructive interference, which results in the blue dots forming a hyperbola. The hyperbola is formed because the constructive interference of the two waves creates a peak, while the destructive interference of the two waves creates a trough.