Two strings of circular cross-section, made of the same material, are stretched to the same tension. A transverse wave passes through each. The speed in the first string, of radius R, is v₁, and in the second, of radius /R2, is v₂. Then (v₂)/(v₁) equals

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(2) 2. The linear density is μ=ρπ r², so v=√T/(ρπ r²)∝1/r. Halving the radius doubles the speed: (v₂)/(v₁)=2.

Two strings of circular cross-section, made of the same material, are stretched to the same tension. A transverse wave passes through each. The speed in the first string, of radius R, is v₁, and in the second, of radius /R2, is v₂. Then (v₂)/(v₁) equals

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