Length of a string of density `rho` and Young's modulus Y under tension is increased by `(1)/(n)` times of its original length If the velocity of transverse and longitudinal vibration of the string is same, find the value of such velocity.

Options

A. `sqrt((Y)/(rhon))`
B. `sqrt((Y)/(rho^((1)/(2))))`
C. `sqrt((Y)/(rho))`
D. `sqrt((Y)/(rhon^((3)/(2))))`

Answer

B

Explanation

`V_1=sqrt((Y)/(rho))=` velocity of longitudinal waves
`V_2=sqrt((T)/(rhoS))=` velocity of transverse waves
`V_1V_2=(1)/(rho)sqrt(Y.Y(trianglel)/(l))=(Y)/(rho)sqrt((trianglel)/(l))`
(As `(T)/(S)=Y(trianglel)/(l)`)
But `(trianglel)/(l)=((l)/(n))/(l)=(1)/(n)`
`V_1V_2=(Y)/(rhon^((1)/(2)))`
`V^2=(Y)/(rhon^((1)/(2)))`
`V=sqrt((V)/(rhon^((1)/(2))))`