A) 277.8m/s
B) 300 m/s
C) 250 m/s
D) 343.4 m/s
Correct Answer: D
Solution :
Given, \[{{l}_{1}}=100\,cm=1\,m\] \[{{l}_{2}}=101\,cm=1.01\,m\] Number of beats per second, \[n=17/20\] Let the velocity of sound is \[v\]and \[{{v}_{1}},{{v}_{2}}\]be the fundamental frequencies of vibrations of two air columns. Then, \[{{v}_{1}}=\frac{v}{4{{l}_{1}}}=\frac{v}{4\times 1}=\frac{v}{4}\] and \[{{v}_{2}}=\frac{v}{4\times 1.01}=\frac{v}{4.04}\] As, \[{{v}_{1}}-{{v}_{2}}=n\] \[\Rightarrow \] \[\frac{v}{4}-\frac{4}{4.04}=\frac{17}{20}\] \[\Rightarrow \] \[v=343.4\,m/s\]
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