Exploring sound waves


Frequently sound is described using terms such as pitch, tone, frequency, intensity or loudness. To understand the origins of these terms as well as to understand the mathematical models used to represent sound, this applet can help you to explore the dynamics of a sound wave.

Modeling a soccer player


A soccer player is on a breakaway, dribbling the ball downfield, parallel to a sideline. From where should she shoot to have the best chance of making a goal? That is, at what point will the angle formed by the player and the two goal posts be the greatest?

The applet below allows you to investigate this problem by changing the location of the player as well as the distance between the player and the goal posts. As you move the player, the angle changes. Where should the player be placed so that the angle is maximized?