ACOUSTIC PULSES SCATTERED BY A RIGID SPHERE IN A FLUID

Physics implemented:

· Eq. 8 — scattered pulseform:
  Ψ(τ) = (1/2π) Re∫ g·f·e^iκτ dκ
  evaluated at N_τ = 700 time points
  (τ from −5 to 35)

· Eq. 11 — far-field form function:
  f(κ) = −(2/κ) Σ P_n(cosθ)(2n+1)·sinη_n·e^iη_n
  N_max = ⌈κ⌉ + 12 terms per frequency

· Eq. 14 — incident pulse spectrum:
  g(κ) = α⁻¹(1−e^−imα) − β⁻¹(1−e^−imβ)
  α = κ+k₀a, β = κ−k₀a, m = 2bπ/k₀a

· Eq. 10 — phase shifts:
  tanη_n = −[(n+1)j_n−κj_n−1] /
              [(n+1)y_n−κy_n−1]

· Grid — κ from 0 to 32π, step Δκ:
  N_κ = ⌊32π/Δκ⌋ frequency points
  Cost: N_κ × N_τ ≈ 2010 × 700 ops