Question

sonometer wire is under tension. the length of the wire between the fixed bridges at the two end is 88cm two movable bridges divided this part of the wire into three segment such that their fundamental frequency are in the ratio 3:1:2 find the length of each segment

Answer 1

As,wire divided in ratio 6:3:2 which gives the length 60:30:20 so HCF will give the λ/2, which is 10 so. λ=20 , Then we know for sonometer , frequency (f) =p/2L(T/µ )^1/2. P- no. of antinode L- length of sonometer wire in meter T-tension µ -mass per unit length And the value, 2L/p=λ So, p=11 L=1.1m ,T=400N, µ=0.01kg/m Putting in formula, f=11/2*1.1(400/0.01)^1/2 f=1000Hz