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BITSAT 2014

Exam: BITSAT
Year: 2014
Subject: Physics
Chapter: Waves and Sound

BITSAT 2014 · Physics · Waves and Sound

When a string is divided into three segments of length l_ 1 , l_ 2...

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

Options

A $\quad \sqrt{v}=\sqrt{v_{1}}+\sqrt{v_{2}}+\sqrt{v_{3}}$
B $v=v_{1}+v_{2}+v_{3}$
C $\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$ .
D $\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_{1}}}+\frac{1}{\sqrt{v_{2}}}+\frac{1}{\sqrt{v_{3}}}$

Correct answer

C. $\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$ .

Step-by-step solution

Fundamental frequency is given by v=

\frac{1}{2 l} \sqrt{\frac{T}{\mu}} \Rightarrow

v \propto

\frac{1}{l} \Rightarrow

P \propto

\frac{1}{v}

Since,

P

divided into

l_{1}, l_{2}

and

l_{3}

segments Here

l=l_{1}+l_{2}+l_{3}

So

\quad \frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}

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