किसी कमानी को `l_(1),l_(2)`तथा`l_(3)` लंबाई के तीन भागो में विभाजित करने में पर उनकी मूल आवृतियाँ क्रमशः `v_(1),v_(2)` तथा`v_(3)` है। तब मूल कमानी की मूल आवृत्ति v होगी -

Options

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

Answer

C

Explanation

` v = 1/(2l) sqrt(T/(m)) rArr v prop 1/l" या "l prop 1/v rArr l = k/l , `
इसी प्रकार `l_(1) = k/(v_(1)) , l_(2) = k/(v_(2))` तथा `l_(3) = k/(v_(3))`
किंतु ` l = l_(2)+l_(3) rArr k/v = k/(v_(1)) +k/(v_(2))+k/(v_(3))`
`rArr 1/v = 1/(v_(1)) +1/(v_(2)) +1/(v_(2))`