The Humming Bridge Cable · AI Generator #GEN-3CDEEC89

Physics

Problem

A suspension bridge cable, modeled as a taut wire of length

L = 240\;\text{m}

and mass per unit length

\mu = 12.5\;\text{kg/m}

, is under tension

T = 2.5 \times 10^6\;\text{N}

. During strong winds, the cable vibrates in its fundamental transverse mode, creating an audible hum. A maintenance engineer stands at one end of the cable and observes the vibration. She then walks along the bridge deck parallel to the cable at a steady speed

v = 8.0\;\text{m/s}

toward the other end while listening to the sound. (a) What frequency does the engineer hear while walking? (b) If she then turns around and walks back toward her starting point at the same speed, what frequency does she hear? (c) What is the difference between the two frequencies she observes? Use

v_{\text{sound}} = 343\;\text{m/s}

for the speed of sound in air.

Browse the problem library