The Humming Fence Wire · AI Generator #GEN-DD91AFF4
Physics
Problem
A rancher notices that when strong winds blow across a particular fence wire, it produces a distinct humming sound. The steel wire has a length of L=50m, mass per unit length μ=0.012kg/m, and is under tension T=480N. The wind creates periodic vortices that detach from the wire at regular intervals, exciting transverse vibrations.
The wire vibrates in its fundamental mode, creating a standing wave with nodes at both ends (where the wire is attached to fence posts). When the rancher measures the frequency of the humming sound, she finds it to be f=22Hz.
(a) What is the wavelength of the transverse wave in the wire?
(b) What is the speed of transverse waves along this wire?
(c) Using your result from part (b), determine the actual tension in the wire and compare it to the given value. Explain any discrepancy.