Each silk thread carries transverse waves with speed c = sqrt(T / mu), where mu is the linear density (dragline silk: radius 1.5 micron, density 1300 kg/m3, so mu = 9.2e-9 kg/m). At T = 25 mN, c is about 1650 m/s. A thread of length L fixed at both ends rings at f_n = n c / (2 L).
The web is a lattice of point masses: radial strands (hub to rim) and spiral strands linking neighbouring radii. Every edge is a spring of stiffness k = T / l0 acting on the out-of-plane displacement u, which gives the discretised 2D wave equation d2u/dt2 = c^2 Laplacian(u). The integrator is symplectic Euler with a time step below the stability limit dt < dx / c.
The spider estimates the prey bearing from which of its radii shows the largest early amplitude. Here the same rule is applied to the 8 radii near the hub for a short window after the pluck; wind adds noise that degrades it.
Simplifications: small amplitudes (linear springs), constant tension, viscous air damping with a fixed coefficient, no in-plane waves, prey strength is an initial displacement not a falling mass, and wind is white noise.