Two vibrating string of the same material but of lengths L and 2L have radii 2r and r respectively.

Question

Two vibrating string of the same material but of lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the string vibrate in their fundamental modes. The one of length L with frequency v1 and the other with respectively v2. The ratio v1/v2 is given by

Accepted Answer

Fundamental frequency is given by

(with both ends fixed)
∴ Fundamental frequency

(for same tension in both string)
where μ = mass per unit of wire
ρ.A (ρ = )
ρ.(πr²) or √μ ∝ r ∴
∴

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