Two stretched wires A and B of the same lengths vibrate independently. If the radius, density and tension of wire A are respectively twice those of wire B, then the fundamental frequency of vibration of A relative to that of B is
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Question

Two stretched wires A and B of the same lengths vibrate independently. If the radius, density and tension of wire A are respectively twice those of wire B, then the fundamental frequency of vibration of A relative to that of B is

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G1 Physics · Accepted Answer

Step 1: For equal string lengths, fundamental frequency f ∝ (1/r)√(T/ρ). Step 2: For wire A, rₐ = 2rᵦ, ρₐ = 2ρᵦ and Tₐ = 2Tᵦ. Step 3: fₐ/fᵦ = (1/2)√[(2)/(2)] = 1/2. Final: B.