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 ration of the denstiy of the first wire to that of the second wire.

Answer

B

Explanation

Let `upsilon_1 = velocity in the 1st string`
`rArr = upsilon_1 = sqrt((T)/(m))`
Because, `m_1` = mass per unit length
`=((p_1 alpha_1)/(I_1))`
` = p_1 alpha_1`
where `alpha_1` = Area of cross - section
`rArr upsilon_1 = sqrt((T)/(p_1 alpha_1)).... (1)`
Let `upsilon_2`= velocity in the second string
`rArr = upsilon_2 = sqrt((T)/(m_2))`
`rArr upsilon_2 = sqrt((T)/(p_2a_2))...(2)`
Given that,
`rArr upsilon_1 = 2upsilon_2`
`rArr = sqrt((T)/(a_1p_1)) = 2sqrt((T)/(a_2p_2))`
`rArr ((T)/(a_1p_1)) = 2((T)/(a_2p_2))`
`rArr (p_1)/(p_2) =(1)/(4)`
`rArr p_1 : p_2 = 1 :4`
`a_1 = a_2`