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 : 

Option 1)  328 ms-1

Option 2) 341 ms-1

Option 3) 322 ms-1

Option 4) 335 ms-1

Answers (1)

String fixed at one end and free from other end -

f_{n}= n\frac{V}{4L}

n= 1,3,5.......

 

- wherein

f_{1}= \frac{V}{4L} is fundamental frequency

 

For f = 512 Hz  - marking 11cm below reference mark

For f = 256 Hz   - marking 27cm below the reference mark

So we have

\frac{\lambda _{1}}{4} = 11cm +e  ........(i)

\frac{\lambda _{2}}{4} = 27cm +e  ..........(ii)

\lambda _{1} = \frac{v}{512}, \lambda _{2} = \frac{v}{256}

from (i) and (ii)

\frac{\lambda _{2}-\lambda _{1}}{4}= 0.16=\frac{v}{4}\left ( \frac{512-256}{512\times 256} \right )

v = 0.16\times 4\times 512\approx 328m/s

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