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  • The length of sonometer wire is <img alt="\mathrm{110 \mathrm{~cm}}" src="https://entrancecorne

The length of sonometer wire \mathrm{A B} is \mathrm{110 \mathrm{~cm}}. where should the two bridge be placed from \mathrm{A} to divide the wire in 3 segments whose fundamental frequencies are in the ratio of \mathrm{1: 2: 3}-
 

Option: 1

\mathrm{30 \mathrm{~cm }\: and \: 90 \mathrm{~cm}}




 


Option: 2

\mathrm{40 \mathrm{~cm} \, and\: 80 \mathrm{~cm}}


Option: 3

\mathrm{60 \mathrm{~cm} \: and \: 90 \mathrm{~cm}}


Option: 4

\mathrm{30 \mathrm{~cm}\: and \: 60 \mathrm{~cm}}


Answers (1)

best_answer

fundamental frequency, \mathrm{f \propto \frac{1}{l}}

Given, \mathrm{f_1: f_2: f_3=1: 2: 3}

 

\mathrm{or \: \frac{l_1}{l_1}: \frac{1}{l_2}: \frac{1}{l_3}=1: 2: 3 \: or \: l_1: l_2: l_3=\frac{1}{1}: \frac{1}{2}: \frac{1}{3}}

\mathrm{or\: l_1: l_2: l_3=6: 3: 2 }

\mathrm{ l_1=\frac{6}{11} \times 110=60 \mathrm{~m} }

\mathrm{ l_2=\frac{3}{11} \times 110=30 \mathrm{~cm} }

\mathrm{ l_3=\frac{2}{11} \times 110=20 \mathrm{~cm} }

Hence option 3 is correct.





 

Posted by

Devendra Khairwa

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