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 $512\, Hz$ 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 $27\, cm$ below the reference mark. The velocity of sound in air, obtained in the experiment, is close to:

• A. $328\,ms^{-1}$
• B. $322\,ms^{-1}$
• C. $341\,ms^{-1}$
• D. $335\,ms^{-1}$

Answer 1

Answer: (A)

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