When a string is divided into three segments of length `l_1,l_2` and `l_3` the fundamental frequencies of these three segments are `f_1,f_2` and `f_3` respectively. The original fundamental frequency `f` of the string is

Options

A. `(1)/(sqrtf)=(1)/(sqrt(f_1))+(1)/(sqrt(f_2))+(1)/(sqrt(f_3))`
B. `sqrtf=sqrtf_1+sqrtf_2+sqrtf_3`
C. `f=f_1+f_2+f_3`
D. `(1)/(f)=(1)/(f_1)+(1)/(f_2)+(1)/(f_3)`

Answer

D

Explanation

Fundamental frequency `f=(v)/(2l)`
`f_1=(v)/(2l_1),f_2=(v)/(2l_2)` and `f_3=(v)/(2l_3)`
`implies(1)/(f)=(1)/(f_1)+(1)/(f_2)+(1)/(f_3)`