A uniform wire of length L, diameter D and density `rho` is stretched under a tension T. The correct relation between its fundamental frequency `'f'`, the length L and the diameter D is

Options

A. `f prop (L)/(D^(2))`
B. `f prop (1)/(D^(2))`
C. `f prop (1)/(LD)`
D. `f prop (1)/(L sqrt(D))`

Answer

C

Explanation

v = `(1)/(2l ) sqrt((T)/(m)) `
Now mass per unit length m `rho . A = rho. (pi D^(2))/(4 ) `
v `= (1)/(2l) sqrt((T)/((pi D^(2))/(4))) = (1)/(l) sqrt((T)/(pi D^(2))) `
For constant tension T, v `prop (1)/(l)`
So correct choice is c.