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Wave Mechanics

Intermediate

Visualize transverse waves, superposition, and interference patterns. Experiment with amplitude, frequency, and wavelength to see how waves combine to create standing waves and beats.

Key Formulas

Wave Equation
y(x,t)=Asin⁡(kx−ωt+ϕ)y(x,t) = A\sin(kx - \omega t + \phi)

General equation for a sinusoidal traveling wave.

Wave Speed
v=fλ=ωkv = f\lambda = \frac{\omega}{k}

Relationship between wave speed, frequency, and wavelength.

Superposition
ynet=y1+y2y_{\text{net}} = y_1 + y_2

When two waves overlap, the resultant displacement is the sum of individual displacements.

Standing Wave
y(x,t)=2Asin⁡(kx)cos⁡(ωt)y(x,t) = 2A\sin(kx)\cos(\omega t)

Pattern formed by two identical waves traveling in opposite directions.

Wave Number
k=2πλk = \frac{2\pi}{\lambda}

Spatial frequency of the wave, relating angular measure to wavelength.

Key Concepts

  • Transverse vs longitudinal waves
  • Principle of superposition
  • Constructive and destructive interference
  • Standing wave nodes and antinodes
  • Wave speed depends on medium properties
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