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JEE Main201912 Jan 2019Evening ShiftPhysicsWaves and SoundActual

A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm bel

Options

  1. A335   m   s - 1
  2. B341   m   s - 1
  3. C322   m   s - 1
  4. D328   m   s - 1

Correct answer

D. 328   m   s - 1

Step-by-step solution

λ 1 4 = 11 + e   ⇒ v 512   ×   4 = 11 + e         . . . ( 1 ) λ 2 4 = 27 + e   ⇒ v 256   ×   4 = 27 + e         . . . ( 2 ) Subtracting the equations, v 256 × 4 × 1 2 = 16   cm = 0 . 16   m ⇒ v = 0.16 × 2 × 4 × 256 = 328   m   s - 1

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