A) \[n={{n}_{1}}\times \,\,{{n}_{2}}\,\times \,\,{{n}_{3}}\]
B) \[\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}\]
C) \[n={{n}_{1}}+\,\,{{n}_{2}}\,+\,\,{{n}_{3}}\]
D) \[n=\frac{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}{3}\]
Correct Answer: B
Solution :
As the spring is cut into three parts. Let \[{{l}_{1}},\,\,{{l}_{2}}\,and\,\,{{l}_{3}}\] are the lengths of these three parts having fundamental frequency of \[{{n}_{1}},\,\,{{n}_{2}}\,and\,{{n}_{3}}\] respectively. Then, \[n\propto \frac{1}{l}\,\,and\,\,l={{l}_{1}}+{{l}_{2}}+{{l}_{3}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}\]
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