A uniform wire of length L and diameter D and density ρ is stretched under a tension T . The correct relation between its fundamental frequency f , the length L and the diameter D is

Question

A uniform wire of length L and diameter D and density ρ is stretched under a tension T . The correct relation between its fundamental frequency f , the length L and the diameter D is, f ∝ 1 L D 2, f ∝ 1 D 2, f ∝ 1 L D, f ∝ 1 L D

MARKS App · Accepted Answer

Since, we know, Frequency, f = n 2 L T m Where, T = tension in the string, L = Length of the string And m = linear mass density of the string. ∴ m = M L = π D 2 2 ⋅ L ⋅ ρ L = π D 2 ρ 4 Thus, f = 1 2 L ⋅ T π D 2 ρ 4 For fundamental frequency, n = 1 f = 1 2 L D 2 T π​ ρ = 1 L D ⋅ T π​ ρ f ∝ 1 L D

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