Amplitude

Definition

In the context of periodic functions (like sine and cosine), Amplitude describes the vertical “size” of the wave.

For $y = A \sin(Bx)$ or $y = A \cos(Bx)$:

• Amplitude: $|A|$
  • How to read: “The absolute value of A.”
  • Meaning: Peak displacement from the midline—always positive even if $A$ is negative (reflection flips the wave but not its height).

Why It Matters

Whether you are analyzing a heartbeat, a radio wave, or an earthquake, amplitude is a “vital sign” of the wave. It allows us to quantify the “power” of an oscillation, which is the foundation of all signal processing.

Core Concepts

• Amplitude: The maximum distance the graph moves above or below its horizontal midline ($y = D$). It is always a positive value ($|A|$).
  • How to read: “The absolute value of A; and y equals D.”
  • Meaning: $|A|$ is half the peak-to-trough distance; $D$ shifts the oscillation center vertically.
• Midline: The horizontal line $y = D$ about which the function oscillates.
  • How to read: “The midline is the line y equals D.”
  • Meaning: The average vertical position around which the wave swings.

Connected Concepts

• Sinusoidal Models
• Graph Transformations
• Periodic Functions
• Simple Harmonic Motion
• Period (Mathematics)