Two strings A and B made of same material are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed `v_A` and on B with speed `v_B`. The ratio `v_A/v_B` is

Options

A. `1/4`
B. `1/2`
C. 2
D. 4

Answer

C

Explanation

According to question, the velocity of wave travelling on string is given by
`v=nlambda=lambda/(2L) sqrt(T/mu)" "(because n=1/(2L)sqrt(T/mu))`
`because v=sqrt(T/(m//l)) Rightarrow v=sqrt((Tl)/m)`
and Young's modulus, `Y= (Txxl)/(ADeltal)`
`therefore (Txxl)/(ADeltaL)`
`therefore vpropsqrtA` (A=Area)
For string A, radius is 2r and for string B radius is r
So, `v_A/v_B=sqrt((4r^2)/r^2) =sqrt4= 2` (therefore Y for both the strings is same.)