The length of the wire between two ends of sonometer is 100 ~cm . What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1: 3: 5 .

Step-by-step solution

According to question Length of wire =L=100 ~cm And ratio of fundamental frequencies =1: 3: 5 aligned L₁: L₂: L₃ & = 1 1 : 1 3 : 1 5 & =15: 5: 3 aligned Let x= comman factor then aligned & 15 x+5 x+3 x=100 & 2 x=100 & x= 100 23 & L₁=15 100 23 & = 1500 23 ~cm & L₂=5 100 23 & = 1500 23 ~cm & aligned aligned L₃ & =3 100 23 & = 300 23 ~cm aligned This shows that bridge should be placed from A at 1500 23 ~cm and 2000 23 ~cm respectively