A) \[\frac{4}{3}{{\ell }_{1}}\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}\]
B) \[\frac{4}{3}{{\ell }_{1}}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\]
C) \[{{\ell }_{1}}\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}\]
D) \[{{\ell }_{1}}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\]
Correct Answer: B
Solution :
[b] Frequency of first overtone in closed pipe, \[v=\frac{3v}{4{{\ell }_{1}}}\sqrt{\frac{P}{{{\rho }_{1}}}}\] ?. (i) Frequency of first overtone in open pipe, \[v'=\frac{1}{{{\ell }_{2}}}\sqrt{\frac{P}{{{\rho }_{2}}}}\] ?. (ii) From equation (i) and (ii) \[\Rightarrow \,\,{{\ell }_{2}}=\frac{4}{3}{{\ell }_{1}}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\]
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