🪔Understanding the Starting Point of a Vibrating String

The two initial conditions provide a complete and unambiguous "freeze-frame" of the string at the moment its vibration begins. The Initial Shape tells us the precise shape of the string (a triangle) at the moment we start observing. The Initial Motion tells us that the string was held motionless at that starting moment.

To understand how a string vibrates over time, we first need a perfect "freeze-frame" snapshot of its very beginning. This snapshot requires answering two simple but crucial questions:

• What is the string's shape at the start?

• Is the string moving at the start?

The mathematics of wave physics uses the variable u to represent the string's vertical height (or transverse displacement) at any horizontal position x and any moment in time t. The text we're studying uses this precise language to answer our two questions. Let's first explore how it defines the string's initial shape.

🎬Programmatic demo

Visualize how the string vibrates over time as a superposition of standing waves | Animated Resultsviadean on Notion