Two uniform strings are made of the same material and are maintained under the same tension. Their radii are r and 2r. If the corresponding transverse wave speeds are v₁ and v₂, what is the ratio v₁/v₂?
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Question

Two uniform strings are made of the same material and are maintained under the same tension. Their radii are r and 2r. If the corresponding transverse wave speeds are v₁ and v₂, what is the ratio v₁/v₂?

Options

G1 Physics · Accepted Answer

For the same material, linear density μ = ρπr². Thus, μ ∝ r². When the radius doubles, μ₂ = 4μ₁. Wave speed is v = √(T/μ). Hence, v₂ = v₁/2. Therefore, v₁/v₂ = 2. Correct option: B.