A resonance tube is old and has a jagged end. It is still used in...

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

512Hz

produces first resonance when the tube is filled with water to a mark

11cm

below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency

256Hz

which produces first resonance when water reaches a mark

27cm

below the reference mark. The velocity of sound in air, obtained in the experiment, is close to

Options

A $335m{s}^{- 1}$
B $341m{s}^{- 1}$
C $322m{s}^{- 1}$
D $328m{s}^{- 1}$

Correct answer

D. $328m{s}^{- 1}$

Step-by-step solution

$\dfrac{{\lambda}_{1}}{4} = 11 + e ⇒ \dfrac{v}{512 \times 4} = 11 + e . . . ( 1 )$

$\dfrac{{\lambda}_{2}}{4} = 27 + e ⇒ \dfrac{v}{256 \times 4} = 27 + e . . . ( 2 )$

Subtracting the equations,

$\dfrac{v}{256 \times 4} \times \dfrac{1}{2} = 16cm = 0 . 16m$

$⇒ v = 0.16 \times 2 \times 4 \times 256$

$= 328m{s}^{- 1}$

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