amplitude

Meaning: Amplitude (A) is the maximum displacement from equilibrium: the distance from the midline to a crest or trough, or to the extreme of an oscillation. For a mass on a spring or a pendulum released from rest, it is the starting displacement. In a sound wave it corresponds to loudness, and in light to brightness. A larger amplitude means more energy stored or carried. The source sets the amplitude, the medium sets the wave speed, and the source sets the frequency.

Equation: E = ½kA², where E is the total mechanical energy of a spring oscillator (J), k is the spring constant (N/m), and A is the amplitude (m). For waves, intensity (W/m²) is proportional to A².

On the MCAT: A typical question doubles the amplitude and asks for the new energy or intensity (four times as large). Another gives a louder sound at the same pitch, so only the amplitude changed. In simple harmonic motion, speed is greatest at equilibrium (vmax = Aω) and zero at ±A, where the restoring force is largest. On a displacement versus time graph, read amplitude as the peak height above the midline. Damping makes the amplitude shrink over time.

Common confusion: Amplitude is not the peak-to-peak height, which is 2A. Changing amplitude does not change frequency, period or wave speed. For an ideal spring or a small-angle pendulum, the period does not depend on amplitude.