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  • A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental freq

A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1:3:4?

Option: 1

 At 36 cm and 84 cm from one end


Option: 2

  At 24 cm and 72 cm from one end


Option: 3

 At 48cm and 96 cm form one end


Option: 4

 

  At 72 cm and 96 cm from one end         


Answers (1)

 

 

 

 

As f=\frac{1}{2 l} *{V} and V=\sqrt{\frac{T}{\mu}}

So V will be constant for sonometer wire

this gives f \propto \frac{1}{l}

l_{1}+l_{2}+l_{3}=114

\begin{aligned} &f_{1}: f_{2}: f_{3}::1: 3: 4\\ &\frac{1}{l_{1}}: \frac{1}{l_{2}}: \frac{1}{l_{3}}::1: 3 \cdot 4 \end{aligned}

l_{1}: l_{2}: l_{3}::1: \frac{1}{3}: \frac{1}{4} \quad \\ \Rightarrow l_{1}: l_{2}: l_{3}::12:4:3

\begin{array}{c} l_{1}=12 x,l_2=4 x,l_{3}=3 x \\ 12 x+4 x+3 x=14 \quad \Rightarrow 19 x=114 \\ x=\frac{114}{19} \Rightarrow x=6 \end{array}

\begin{aligned} &l_{1}=72 \mathrm{cm}, \quad l_{2}=24 \mathrm{cm}\\ &l_{3}=18 \mathrm{cm} \end{aligned}

bridges be placed  At 72 cm and 96 cm from one end

Posted by

Sumit Saini

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