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If a tuning fork of frequency ( f 0 ) 340 Hz and tolerance ± 1 % is used in the resonance column method for determining the speed of sound. If the first and the second resonance are measured at l ⁡ 1 = 2 4.0 cm and l ⁡ 2 = 74.70 cm , then the permissible error in speed of sound is

Options

  1. A1 . 2 %
  2. B1 . 8 %
  3. C1 %
  4. D0 . 8 %

Correct answer

A. 1 . 2 %

Step-by-step solution

V = 2 f 0 l 2 - l 1 let l 2 - l 1 = x l 1 = 24.0 + ¯ 0.1 cm l 2 = 74.70 + ¯ 0.01 cm l 2 - l 1 = 50.70 + ¯ 0.11 cm Δ x x = 0.11 50.70 Δ x % = 0.11 50.70 × 100 = 0.22% Δ V % = Δ f 0 % + Δ x % = 1.22 % = 1.2 %

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