The Resonant Earthquake Detector · AI Generator #GEN-0FAFC2DB

Physics

Problem

A seismologist designs a novel earthquake detector consisting of a thin vertical steel wire of length L=2.4  mL = 2.4\;\text{m} and mass m=15  gm = 15\;\text{g}, fixed at the top and with a small mass M=180  gM = 180\;\text{g} attached at the bottom. The wire has tension T=72  NT = 72\;\text{N}. When an earthquake occurs, horizontal ground vibrations create transverse waves that propagate up the wire. During a particular earthquake, the ground oscillates horizontally with frequency f=25  Hzf = 25\;\text{Hz} and amplitude A0=2.0  mmA_0 = 2.0\;\text{mm}. The seismologist observes that the bottom mass exhibits dramatic oscillations with amplitude Amax=4.8  cmA_{max} = 4.8\;\text{cm}, indicating resonance with one of the wire's natural modes. Find the speed of transverse waves on this wire.

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