KVPY Sample Paper KVPY Stream-SX Model Paper-6

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity in air. A tuning fork of frequency 512 HZ produces first resonance when the tube is filled with mark 11 cm below a reference mark, near end of the tube. The experiment is repeated fork of frequency 256 Hz which prod' resonance when water reaches a mark 27 the reference mark. The velocity of obtained in the experiment, is close to:

A) \[322\,m{{s}^{-1}}\]

B) \[341\,m{{s}^{-1}}\]

C) \[335\,m{{s}^{-1}}\]

D) \[328\,m{{s}^{-1}}\]

Correct Answer: D

Solution :

\[\frac{{{\lambda }_{1}}}{4}=11\,cm.+e\] \[\Rightarrow \] \[\frac{\nu }{512\times 4}=11\,cm.+e\]? (1)

\[\frac{{{\lambda }_{2}}}{4}=27cm.+e\] \[\Rightarrow \] \[\frac{\nu }{256\times 4}=27cm.+e\] ? (2)

Equation \[(2)-(1)\frac{\nu }{256\times 4}\times \frac{1}{2}-0.16\]

\[\nu =0.16\times 2\times 4\times 256=327.68\,\text{m/s}\]