When a string is divided into three segments of length l 1, l 2 and l 3 the fundamental frequencies of these three segments are v₁, v₂ and v₃ respectively. The original fundamental frequency ( v) of the string is (a) √(v) = √(v₁) + √(v₂) + √(v₃) (b) v = v₁ + v₂ + v₃ (c) 1/v = 1/v₁ + 1/v₂ + 1/v₃ (d) 1/√(v) = (1)/(√(v₁)) + (1)/(√(v₂)) + (1)/(√(v₃))

Answer: (c). Same tension and μ: v ∝ 1/l, so l = k/v. l = l₁ + l₂ + l₃ ⇒ 1/v = 1/v₁ + 1/v₂ + 1/v₃. So the answer is (c).

When a string is divided into three segments of length l 1, l 2 and l… | NEET 2012 (AIPMT, Prelims)

Q106NEET 2012 · AIPMT · PRELIMSEasy

Stationary Waves & Vibrating Strings

When a string is divided into three segments of length $l$ 1, $l$ 2 and $l$ 3 the fundamental frequencies of these three segments are $v_1, v_2$ and $v_3$ respectively. The original fundamental frequency ( $v$ ) of the string is

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Answer: (c)

Same tension and $\mu$ : $v \propto \dfrac{1}{l}$ , so $l = \dfrac{k}{v}$ .
$l = l_1 + l_2 + l_3 \Rightarrow \dfrac{1}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2} + \dfrac{1}{v_3}$ .
So the answer is (c).

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