Wave Equation

★★★★☆Undergraduate

📖Definition

Wave equation is a PDE describing wave propagation. Applies to sound, light, water waves, etc.

(∂² u)/(∂ t²) = c² ∇² u

General wave equation

(∂² u)/(∂ t²) = c² (∂² u)/(∂ x²)

1D wave equation

u(x,t) = f(x - ct) + g(x + ct)

General solution (d'Alembert)

u(x,t) = Asin(kx - ω t)

Sinusoidal solution

예제 1

Wave equation for sound at 340m/s?

예제 2

Wave with λ=2m, T=0.5s. Speed?

Discovered by: Jean le Rond d'Alembert (1746)

Derived while studying vibrating strings

Sound propagation modeling

Seismic wave analysis

EM waves

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