A sonometer wire has a length of 114 cm between two fixed ends, where should two bridges be placed to divide the wire into three segments whole fundamental frequencies are in the ratio 1:3:4?

In case of a given wire under constant tension    Fundamental frequency of vibration f ∝1l ∴l1:l2:l3=11:13:14=12:4:3 l1=1219×114⇒l1=72 cm l2=24 cm l3=18 cm ∴  First bridge is to be placed 72 cm from one end.   Second bridge is to be placed 72+24=96​ cm  from one end