question_answer

If a string of length 133 cm is divided in 3 segments having fundamental frequency in the ratio of \[1:3:4\] then lengths of these segments are-

A) 84 cm, 28cm, 21 cm

B) 90 cm, 22 cm, 21 cm

C) 78 cm, 34 cm, 21 cm

D) 50 cm, 72 cm, 11 cm

Correct Answer: A

Solution :

\[{{f}_{1}}:{{f}_{2}}:{{f}_{3}}=1:3:4\] \[f\propto \frac{1}{l}\,\,\therefore \,\,{{l}_{1}}:{{l}_{2}}>:{{l}_{3}}=1:\frac{1}{3}:\frac{1}{4}\,\,=\,\,12\,\,:\,\,4\,\,:\,\,3\] \[19x\,\,=\,\,133\,\,\,\,\Rightarrow \,\,x=7\,cm\] \[\therefore \,\,{{l}_{1}}=84\,cm:{{l}_{2}}\,\,=\,\,28\,cm:\,\,{{l}_{3}}=21\,cm\]