The Quantum Lighthouse · AI Generator #GEN-AE0B642A
Physics · modern-physics
Problem
A research station uses a novel lighthouse system where a rotating cesium-137 source emits gamma rays with energy Eγ=662keV. The source rotates at ω=2.0rad/s and is located at height h=50m above sea level. A detector on a ship measures the gamma ray frequency as the lighthouse beam sweeps past.
Due to the rotation, when the beam points directly toward the ship, the source has a radial velocity component toward the detector. At the moment when the lighthouse beam is tangent to a circle of radius R=30m centered at the lighthouse base and the beam points toward the ship, calculate the fractional frequency shift f0Δf observed by the detector due to the relativistic Doppler effect.
Assume the ship is at the same height as the tangent point and very far away, so the beam direction is essentially horizontal.