If `v_(1) , v_(2) and v_(3)` are the fundamental frequencies of three segments of stretched string , then the fundamental frequency of the overall string is

Options

A. `v_(1) + v_(2) + v_(3)`
B. `[(1)/(v_(1)) + (1)/(v_(2)) + (1)/( v_(3))]^(-1)`
C. `v_(1) v_(2) v_(3)`
D. `[v_(1) v_(2) v_(3)]^(1//3)`

Answer

B

Explanation

`l = l_(1) + l_(2) + l_(3)` [ `because v prop (1)/(l)`]
`(k)/(v) = (k)/(v_(1)) + (k)/(v_(2)) + (k) + (k)/( v_(3))`
`(1)/(v) = (1)/(v_(1)) + (1)/( v_(2)) + (1)/(v_(3))`
`v = [(1)/(v_(1)) + (1)/( v_(2)) + (1)/(v_(3))]^(-1)`