When a string is divided into three segments of
lengths `l_(1),l_(2) and l_(3)` the fundamental frequencies of
these three segments are `v_(1), v_(2) and v_(3)` respectively.
The original fundamental frequency (v) of the string is

Options

A. `v=v_(1)+v_(2)+v_(3)`
B. `(1)/(v)=(1)/(v_(1))+(1)/(v_(2))+(1)/(v_(3))`
C. `(1)/(sqrt(v))=(1)/(sqrt(v_(1)))+(1)/(sqrt(v_(2)))+(1)/(sqrt(v_(3)))`
D. `sqrt(v)=sqrt(v_(1))+sqrt(v_(2))+sqrt(v_(3))`

Answer

B

Explanation

`(lambda_(1))/(2)=l_(1)implieslambda_(1)=2l_(1)`, `v_(1)=(v)/(lambda_(1))=(v)/(2l_(1))`
`(lambda_(2))/(2)=l_(2)=2l_(2)`, `v_(2)=(v)/(lambda_(2))=(v)/(2l_(2))`
`(lambda_(3))/(2)=l_(3)implieslambda_(3)=2l_(3)`, `v_(3)=(v)/(lambda_(3))=(v)/(2l_(3))`
`(1)/(v_(1))+(1)/(v_(2))+(1)/(v_(3))=(2l_(1))/(v)+(2l_(2))/(v)+(2l_(3))/(v)`
`(2l_(1)+2l_(2)+2l_(3))/(v)=(1)/(v)`