A Michelson interferometer sees the chirp of two merging black holes. Left: the optical layout (arm motion exaggerated). Right: how a ring of free masses is squeezed by the passing wave.
A binary of masses m1, m2 radiates gravitational waves that carry the orbit inward. Everything at leading (Newtonian quadrupole) order depends on the chirp mass Mc = (m1m2)3/5/(m1+m2)1/5. With τ the time to merger the wave frequency is f = (1/π)(5/(256 τ))3/8 (GMc/c³)-5/8, equivalently df/dt = (96/5) π8/3 (GMc/c³)5/3 f11/3; the phase is Φ = Φc - 2 (5GMc/c³)-5/8 τ5/8.
The strain amplitude is A = (4/d)(GMc/c²)5/3 (π f/c)2/3 with polarisations h+ = A (1+cos²ι)/2 cosΦ, h× = A cosι sinΦ. The arms change length by ΔLx = +hL/2, ΔLy = -hL/2 so the difference is ΔL = hL (4 km arm and h = 10-21 gives 4×10-18 m). A Michelson at its dark fringe passes P/P0 = sin²(δφ/2) with δφ = 4πΔL/λ.
Simplifications: the inspiral stops at the innermost stable circular orbit fISCO = c³/(63/2πGM) and the merger and ringdown are a schematic damped sinusoid, not numerical relativity; no spin, no cosmological redshift, optimal sky position, white noise instead of the real noise spectrum, no arm cavities. The drawn mirror motion and fringe phase are exaggerated by many orders of magnitude.