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A sonometer wire has a length of 114 cm between its two fixed ends. Where should the two briges be places so as todivide the wire into three segments, whos fundamental frequencies are in the ratio `1:3:4?` |
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Answer» Here, `L=114cm`. Let the two bridges divide the entire length in three parts of lengths `l_(1), l_(2), l_(3)` such that `n_(1):n_(2):n_(3)=1:3:4.` As `nprop(1)/(l), ` therefore, `l_(1):l_(2):l_(3)=(1)/(1):(1)/(3):(1)/(4)=12:4:3.` `l_(1)=(Lxx12)/((12+4+3))=(114)/(19)xx12=72cm` `l_(2)=(114xx4)/(19=24cm` , `l_(3)=(114xx3)/(19)=18cm` Hence two bridges must be placed at 72cm and `(72+24)=96cm` from one end. |
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