🪔How Gravity Gently Shapes a Vibrating String: A Simple Look at the Wave Equation

Gravity as an External Force: Gravity adds a constant downward term to the standard wave equation, representing a steady external force on every part of the string. The Stationary Shape: By ignoring vibrations and looking only at the effects of tension and gravity, we find the string settles into a slight parabolic curve. Tension is Key: This entire model is an excellent approximation, but only for strings that are pulled very tight. In these cases, the restoring force from tension is vastly stronger than the force of gravity, ensuring the string's sag and its slope remain very small.

Have you ever wondered what happens to a simple vibrating string, like on a guitar or violin, when we account for the constant, gentle pull of gravity? While it might seem like a tiny effect, physics gives us the tools to describe it precisely.

We will explore this question using one of the most famous tools in physics: the wave equation. By adding a small term to represent gravity, we can see how the string's behavior changes. Our goal is to understand the core concepts and the beautiful physics at play, not to get lost in complex calculations.

🎬Programmatic demo

how the string's equilibrium is fundamentally shifted by the constant external force | Animated Resultsviadean on Notion