Rankers Physics

Uncategorized: Practice Problem & Solution

44. When a string is divided into three segments of length $l_1$, $l_2$ and $l_3$ the fundamental frequencies of these three segments are $v_1$, $v_2$ and $v_3$ respectively. The original fundamental frequency ($v$) of the string is: (2012 Pre)
$\sqrt{v} = \sqrt{v_1} + \sqrt{v_2} + \sqrt{v_3}$
$v = v_1 + v_2 + v_3$
$\frac{1}{v} = \frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3}$
$\frac{1}{\sqrt{v}} = \frac{1}{\sqrt{v_1}} + \frac{1}{\sqrt{v_2}} + \frac{1}{\sqrt{v_3}}$

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

The fundamental frequency is inversely proportional to the length of the string ($l \propto 1/v$). Since the total length $l = l_1 + l_2 + l_3$, substituting lengths with reciprocal frequencies gives $\frac{1}{v} = \frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3}$.

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