C16 - Wave Motion

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1

wave function f(x,t)

f(x,t) = f(x-vt) = Asin(kx-ωt+Φ)

k = wave # = 2π/λ

2

wave speed

v = λf = λ/T = sqrt(T/μ) = ω/k

3

transverse & longitudinal

long: F || v_wave

tran: F ⊥ v_wave

4

transverse qtys

v_y= -ωAcos(kx-ωt+Φ)

a_y = -ω²Asin(kx-ωt+Φ)

5

wave energy (strings)

K_λ = U_λ = (ω²A²μλ)/4

E_λ = (ω²A²μλ)/2

P = (ω²A²μv)/2

6

linear wave eqn