The length and diameter of a metal wire is doubled the fundamental frequency of vibration will change from n to (tension being kept constant and material of both the wires is same)

Options

A. `n/4`
B. ` n / 8`
C. `n/12`
D. ` n/16`

Answer

A

Explanation

`n = 1/(2L) sqrt(T/m) = 1/(2L) sqrt(T/(pir^(2) rho)) = 1/(2 L r) sqrt(T/(pi rho))`
For the wire ,T and `rho` are the same .
`:. n propto 1/(Lr) :. n_(2)/n_(1) = (L_(1)r_(1))/(L_(2)r_(2)) = ( 1/2 ) ( 1/2) = 1/4`
` :. n_(2) = n_(1)/4 " or " n_(2) = n/4`