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

Answer 1

The correct option is D $328m{s}^{-1}$

Given,
Two tuning forks of frequencies $f_1$ and $f_2$ be $512Hz$ and $256Hz$ respectively. Corresponding to each frequency’s paths, the lengths of the first resonance air column are $11cm$ and $27cm$ respectively.

In case of a closed pipe,

For frequency $f_1$,

$\frac{{\lambda }_1}{4}=11+e$

$\Rightarrow \frac{\upsilon }{512\times 4}=11+e\dots \left(i\right)$

For frequency $f_2$,

$\frac{{\lambda }_2}{4}=27cm+e$

$\Rightarrow \frac{v}{256\times 4}=27+e\dots \left(ii\right)$

Equation $\left(ii\right)-\left(i\right)$,

$\frac{\upsilon }{256\times 4}\times \frac{1}{2}=0.16$

$\upsilon =0.16\times 2\times 4\times 256=327.68m/s$

$\approx 328m/s$