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Grade 12Wave Optics

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.

karthik

8 Years agoGrade 12

3 Answers

Saurabh Koranglekar

6 Years ago

Saurabh Koranglekar

6 Years ago

Arun

6 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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