Mechanical Waves: Energy Distribution in a Traveling Wave

Why Kinetic & Potential Energy Are Actually In Phase

Most students mistakenly believe that a traveling wave stores its maximum potential energy at the peak (amplitude), similar to a pendulum or a mass on a spring. This interactive simulation proves otherwise. Dive into the mechanics of a transverse wave on a string and visualize exactly how energy flows through a medium.

How to Use the Simulation:

The Control Deck: Use the sliders at the bottom to manipulate the fundamental properties of the wave. Adjust the Tension (T) and Mass Density (μ) to see how they dictate the wave speed, following the relationship v = √(T/μ).

Track the Particle: Focus on the single orange string segment. Watch the Energy Bar Chart floating next to it. Notice how the Total Energy (TE) fluctuates as the wave passes through.

Vector Analysis: Observe the u (particle velocity) vector. Notice it is perpendicular to the wave's propagation velocity (v).

Slow It Down: Use the Slow Motion slider (set to 0.1× by default) and the Pause button to freeze time and analyze the exact moment a crest or trough passes through.

Key Physics Insights:

The Phase Surprise: Unlike Simple Harmonic Motion (SHM) where Kinetic Energy (KE) and Potential Energy (PE) swap back and forth, in a traveling wave, they oscillate in phase.

Max Energy at Equilibrium: Notice that both KE and PE bars hit their maximum height when the particle crosses the equilibrium line (y = 0). This is where the string has the highest transverse velocity (max KE) and the steepest slope/stretch (max PE).

Zero Energy at Extremes: At the crests and troughs (y = ±A), the particle momentarily stops (KE = 0) and the string is locally flat/unstretched (PE = 0). This demonstrates that energy is not stored at the peaks, but is being transported through the medium.

Keep going:

Equations & Traps deck · Mind Maps bundle