A string of length L is fixed at one end and perfectly free at the other end. Transverse waves on the string have speed v. Which expression gives the allowed natural frequencies?
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Question

A string of length L is fixed at one end and perfectly free at the other end. Transverse waves on the string have speed v. Which expression gives the allowed natural frequencies?

G1 Physics · Accepted Answer

The fixed end is a node and the free end is an antinode. Therefore the allowed lengths satisfy L = (2n−1)λₙ/4, where n = 1,2,3,... Thus, λₙ = 4L/(2n−1). Hence, fₙ = (2n−1)v/(4L). Correct option: B.