This simulator drives a traveling wave whose amplitude and frequency you control directly, and computes relative energy and power using the standard proportionality that wave energy scales with the square of amplitude (and power additionally scales with the square of frequency). A live energy bar and a pulsing glow at a fixed observation point turn those numbers into something you can see and feel change.
• A live animated wave whose amplitude and frequency you set directly with sliders. • A relative energy bar that fills according to (A/A₀)², using your starting amplitude as the baseline. • A pulsing glow at a fixed point on the wave path whose peak brightness and pulse strength scale with relative power, (A/A₀)²·(f/f₀)². • Live numeric readouts for both relative energy and relative power so you can check the math against what you see.
For most mechanical and electromagnetic waves, the energy carried is proportional to the square of the amplitude, not the amplitude itself. That means doubling amplitude quadruples the energy, and tripling amplitude makes it nine times larger. This is why, for example, doubling the loudness (amplitude) of a sound source takes far more than double the driving power, and why small amplitude increases near a resonant peak can represent a large jump in stored or delivered energy.
Wave energy is proportional to the square of amplitude (E ∝ A²). Doubling the amplitude of a wave quadruples the energy it carries, not merely doubles it.
Power is proportional to A²f², so doubling both amplitude and frequency multiplies power by 2² × 2² = 16.
Because the bar tracks (A/A₀)², a squared relationship — small increases in amplitude near the top of the slider range produce disproportionately large jumps in relative energy, which is exactly the nonlinear behavior real waves show.
It shows a simplified relative-energy proportionality for a generic wave, not a full accounting of an actual physical medium's density, elasticity, or absolute energy units — the readouts are ratios relative to your chosen baseline amplitude and frequency, not physical joules.