Questions:

16.1. Run the simulation to see how a Gaussian pulse reflects off the two different boundaries. How is a pulse reflected from a fixed boundary different from one reflected from a free boundary?

16.2. Now check the sine wave check box to see what happens when a sine wave hits the two types of boundaries. What is the end result in these cases? (Hint: Go back to simulation 10 and add two identical waves moving in opposite directions.)

16.3. Although the reflecting sine waves in both cases interacts with the incoming wave to form a standing waves there is a slight difference between the two. Which case has a node at the boundary and which has an anti-node at the boundary? (Nodes and anti-nodes were defined in simulation 10.)

A wave reflected from a stiff or fixed boundary is said to have a phase shift of 180^o (or π radians). This means a pulse will invert itself on reflection and the first anti-node of a standing wave will occur 180^o from the boundary. If the boundary is soft the first anti-node occurs at the boundary. As we will see shortly, other kinds of waves also experience a phase shift on reflection from some kinds of boundaries. For example when light in air reflects from a material that is more optically dense (such as a glass) there is a phase change of 180^o but when light in glass reflects from a glass/air boundary there is no phase change since the light is going from a more optically dense material (glass) to a less optically dense material (air).