A) 36cm
B) 54cm
C) 108cm
D) 180cm
Correct Answer: A
Solution :
For a closed pipe, the length \[(l)\] of vibrating air column is given by \[l+e=(2\,r+1)\frac{\lambda }{4}\] where e is end correction and \[\lambda \]is wavelength. The length corresponding to r be \[{{l}_{1}}=45\,cm\] and that corresponding to r + 3 be\[{{l}_{1}}=99\,cm\]. Intermediate two values being (r + 1) and (r + 2). \[\therefore \] \[{{l}_{1}}+e=(2\,r+1)\frac{\lambda }{4}\] ... (i) \[{{l}_{2}}+e=[2\,(r+3)+1]\frac{\lambda }{4}=(2\,r+7)\frac{\lambda }{4}\] ... (ii) Subtracting Eq. (i) from Eq. (ii), we get \[{{l}_{2}}-{{l}_{1}}=6\frac{\lambda }{4}\] \[\Rightarrow \] \[\lambda =\frac{2}{3}({{l}_{2}}-{{l}_{1}})=\frac{2}{3}(99-45)\] \[=\frac{2}{3}\times 54=36\,cm\]
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