Question

A resonance tube is old and has jagged end. It is still used in the laboratory to determine 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:

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

Answer 1

Answer: (A)

$\frac{{\lambda }_1}{4}=11cm$ so ,
$\frac{v}{512\times 4}=11cm$
$\frac{{\lambda }_2}{4}=27cm$ so ,
$\frac{v}{256\times 4}=27cm$
$(2)-(1)$ $\frac{v}{256\times 4}\times 0.5=0.16$
$v=0.16\times 2\times 4\times 256$
$v=328m/s$
$\frac{v}{256\times 4}\times 0.5=0.16$
$v=0.16\times 2\times 4\times 256$
$v=328m/s$