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  • A sonometer wire has a length of 114cm between two fixed ends. Where should two bridges placed so as to divide the wire into three segments whose fundamental frequencies are in the ration 1:3:

A sonometer wire has a length of 114cm between two fixed ends. Where should two bridges placed so as to divide the wire into three segments whose fundamental frequencies are in the ration 1:3:4

Option: 1

l_1=72cm, l_2=24cm, l_3=18cm


Option: 2

l_1=60cm, l_2=40cm, l_3=14cm


Option: 3

l_1=52cm, l_2=30cm, l_3=32cm


Option: 4

l_1=65cm, l_2=30cm, l_3=19cm


Answers (1)

best_answer

\\Use,\ f \propto \frac{1}{l}\\ \therefore l_1: l_2: l_3=\frac{1}{f_1}: \frac{1}{f_2}: \frac{1}{f_3}=\frac{1}{1}: \frac{1}{3}: \frac{1}{4} \\

\\\text { or } l_1: l_2: l_3=12: 4: 3 \\ l_1=\frac{12}{13} \times 114=72 \mathrm{~cm} . \\ l_2=\frac{4}{1} \times 114=24 \mathrm{~cm},\\ \quad l_3=\frac{3}{19} \times 114=18 \mathrm{~cm} .

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Rishi

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