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. `fprop(1)/(LD)`
B. `fprop(1)/(Lsqrt(D))`
C. `fprop(1)/(D^(2))`
D. `fprop(1)/(LD^(2))`

Answer

A

Explanation

The fundamental frequency is
`f=(1)/(2L)sqrt((T)/(mu))`
where `mu` is the mass per unit length of the wire
`f=(1)/(2L)sqrt((T)/(rhopi(D^(2))/(4)))=(1)/(2L)sqrt((4T)/(rhopiD^(2)))=(1)/(LD)sqrt((T)/(pirho)) ` or `fprop(1)/(LD)`