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

Accoesing 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))`
`therefore v= sqrt(T/(m//l))rArrv+ sqrt((Tl)/m)`
and Young' modulus, `Y=(Txxl)/(ADeltal)` `therefore Txx l = Y A Delta l` ltbtrgt ` therefore v prop sqrt(A)` (A=Area)
For string A, radius is 2r and for string B redius is r. ltbbrgt So, `v_(A)/v_(B)=sqrt((4r^(2))/r^(2))=sqrt(4)=2`
[`therefore` Y for both the strings is same. ]