A wire of length 
is made by joining two wires 
and 
of same lengths but different radii 
and 
and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire 
is 
and that in 
is 
then the ratio 
is:
Text Solution
Verified by ExpertsB
Let mass per unit length of wires are 
and 
respectively.
Materials are same, so density 
is same.
and 
Tension in both are same 
, let speed of wave in wires are 
and 
radius 
radius 
Frequency at which both resonate is L.C.M. of both frequencies i.e. 
.
Hence number of loops in wires are 1 and 2 respectively
So, ratio of number of antinodes is 
.
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