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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 10335 Points
4 years ago
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Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
576-386_3.PNG
Arun
25750 Points
4 years ago
Let the velocity of the 1st string will be V1​
⇒v1​=m1​T​​
 because m1​= mass per unit lenght = l1​ρ1​a1​l1​​=ρ1​a1​
where a1​ = area pf the cross section
⇒v1​=ρ1​a1​T​​ 
Let the velocity of the 2nd string will be V2​
⇒v2​=m2​T​​
⇒v2​=ρ2​a2​T​​ 
given that V1​=V2​
⇒ρ1​a1​T​​=2ρ2​a2​T​​
⇒ρ2​ρ1​​=41​
⇒ρ1​:ρ2​=1:4 ( because a1​=a2​)

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