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Radhika Batra Grade: 11
        Two wires of different densities but same area of cross section are soldered together at one end and 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 second wire. 
3 years ago

Answers : (1)

Deepak Patra
askIITians Faculty
474 Points
										Sol. Let v1 = velocity in the 1st string

⇒ v1 = √(T /m1)
Because m1 = mass per unit length = (1a1l1 / l1) = 1a1 where a1 = Area of cross section
⇒ v1 = √(T / p1a1) …(1)
Let v2 = velocity in the second string
⇒ v2 = √(T /m2 )
⇒ v2 = √(T / p2a2 ) …(2)
Given that, v1 = 2v2
⇒ √(T / p1a1) = 2 √(T / p2a2 ) ⇒ (T/a1p1) = 4(T/a2p2)
⇒ p1/p2 = 1/4 ⇒ p1 : p2 = 1 : 4 (because a1 = a2)
3 years ago
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