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Two wires of different densities but same area of cross section are soldered together at one end are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.

Two wires of different densities but same area of cross section are soldered together at one end are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.

Grade:12

3 Answers

Saurabh Koranglekar
askIITians Faculty 10336 Points
2 years ago
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Saurabh Koranglekar
askIITians Faculty 10336 Points
2 years ago
576-386_3.PNG
Arun
25758 Points
2 years ago
Let the velocity of the 1st string will be V1
v1=m1T
 because m1= mass per unit lenght = l1ρ1a1l1=ρ1a1
where a1 = area pf the cross section
v1=ρ1a1T 
Let the velocity of the 2nd string will be V2
v2=m2T
v2=ρ2a2T 
given that V1=V2
ρ1a1T=2ρ2a2T
ρ2ρ1=41
ρ1:ρ2=1:4 ( because a1=a2)

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