A uniform string is vibrating with a fundamental frequency ' n '. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

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​ l 2 ​ = 2 l 1 ​ , R 2 ​ = 2 R 1 ​ , T 1 ​ = T 2 ​ n = 2 l 1 ​ m T ​ ​ Where, m = mass per unit length = l ( nR 2 l ) ρ ​ ∴ m ∝ R 2 ∴ n 1 ​ n 2 ​ ​ = l 2 ​ l 1 ​ ​ × R 2 ​ R 1 ​ ​ ∴ n 1 ​ n 2 ​ ​ = 2 l 1 ​ l 1 ​ ​ × 2 R 1 ​ R 1 ​ ​ ∴ n 2 ​ = 4 n 1 ​ ​ = 4 n ​ ​

Physics - Wave on String Question with Solution | TestHub

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