Q. Three similar wire of frequency $n_{1},n_{2}$ and $n_{3}$ are joined to make one wire. Its frequency will be
A) $n = n_{1} + n_{2} + n_{3}$
B) $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$
C) $\frac{1}{\sqrt{n}} = \frac{1}{\sqrt{n_{1}}} + \frac{1}{\sqrt{n_{2}}} + \frac{1}{\sqrt{n_{3}}}$
D) $\frac{1}{n^{1}} = \frac{1}{n_{1}^{2}} + \frac{1}{n_{2}^{2}} + \frac{1}{n_{3}^{2}}$
Explanation
(b) $n = \frac{1}{2l}\sqrt{\frac{T}{m}} \Rightarrow n_{1}l_{1} = n_{2}l_{2} = n_{3}l_{3} = k$
$l_{1} + l_{2} + l_{3} = l \Rightarrow \frac{k}{n_{1}} + \frac{k}{n_{2}} + \frac{k}{n_{3}} = \frac{k}{n}$
$\Rightarrow \frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.