The Relativistic Radar Trap · AI Generator #GEN-4C96F8B9

Physics

Problem

A futuristic police radar system operates by sending out electromagnetic pulses and measuring the time delay of reflections from moving vehicles. The radar station is located on a straight highway and emits pulses at regular intervals of Δt0=2.0×10−6  s\Delta t_0 = 2.0 \times 10^{-6}\;\text{s} as measured in the station's rest frame. A spacecraft traveling at speed v=0.60cv = 0.60c approaches the radar station along the highway. The radar operator observes that the time interval between receiving consecutive reflected pulses from the spacecraft is Δtobs=1.2×10−6  s\Delta t_{\text{obs}} = 1.2 \times 10^{-6}\;\text{s}. (a) What is the time interval between consecutive pulse emissions as measured in the spacecraft's rest frame? (b) From the spacecraft's perspective, what is the time interval between the arrival of consecutive pulses from the radar station? (c) Verify your answer to part (b) by calculating what time interval the radar operator should observe between reflected pulses, given the spacecraft's speed.

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