Question

The length of a sonometer wire between two fixed ends is 110cm. Where should the two bridges the placed so as to divide the wire into three segments, whose fundamental frequencies are in the ration` 1:2:3?`

Answer 1

Here, total length of the wire,
`L=110 cm, v_(1):v_(2):v_(3)=1:2:3`
If `l_(1),l_(2),l_(3)` are the lengths of the three parts, then as `vprop(1)/(l)`
`:. l_(1):l_(2):l_(3)=(1)/(1):(1)/(2):(1)/(3) =6:3:2`
sum of the ratios`=6+3+2=11`
`:. l_(1)=(L)/(11)xx6=(110)/(11)xx6=60cm ,`
`:. l_(2)=(L)/(11)xx3=(110)/(11)xx3=30cm ,`
`:. l_(2)=(L)/(11)xx2=(110)/(11)xx2=20cm,`
Hence , the bridges should be placed at 60cm and 90 cm from the zero end of the wire.