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NEETPhysicsWaves and Sound

Answer the following by appropriately matching the lists based on the information given in the paragraph. A musical instrument is made using four different metal strings, 1 , 2 , 3 and 4 with mass per unit length μ , 2 μ , 3 μ and 4 μ respectively. The instrument is played by vibrating the strings by varying the free length in between the range L 0 and 2 L 0 . It is found that in string- 1 μ at free length L 0 and te

Options

  1. Aa - p , b - q , c - t , d - u
  2. Ba - t , b - q , c - r , d - u
  3. Ca - p , b - q , c - r , d - t
  4. Da - p , b - r , c - t , d - u

Correct answer

A. a - p , b - q , c - t , d - u

Step-by-step solution

Case 1 . L = L 0 , T = T 0 , f = f 0 f 1 = 1 2 L 0 T 0 μ = f 0 (fundamental frequency of vibration in string fixed at both ends) Case 2 . L = 3 L 0 2 , T = T 2 , f 2 = f 0 f 2 = 3 2 × 3 L 0 2 T 2 2 μ = f 0 ⇒ f 0 = 1 2 L 0 T 2 μ ⇒ T 2 = T 0 2 Case 3 . L = 5 L 0 4 , T = T 3 , f 3 = f 0 f 3 = 5 2 × 5 L 0 4 T 3 3 μ = f 0 ⇒ f 0 = 2 3 L 0 T 3 μ ⇒ T 3 = 3 T 0 16 Case 4 . L = 7 L 0 4 ⇒ f 4 = 14 2 × 7 L 0 4 T 4 4 μ = f 0 ⇒ f 0 = 2 L 0 T 4 μ ⇒ T 4 = T 0 16

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