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Two sttings A and B length l(A) and l(B)...

Two sttings A and B length `l_(A) and l_(B) ` and carry masses `M_(A) and M_(B)` at their lower ends . The upper ends being supported by rigid supports. If `n_(A) and n_(B)` are the frequencies of their vibrations and `n_(A) = 2n_(B)` , then

A

`l_(A) = (l_(B))/(4)`

B

`l_(A) = 4l_(B)`

C

`l_(A) = 2l_(B)` & `M_(A) = 2M_(B)`

D

`l_(A) = (l_(B))/(2) & M_(A) = (M_(B))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`f = (1)/(2 pi) sqrt((g)/(l))`
`f prop (1)/(sqrt(l))`
`(f_(A))/(f_(B)) = sqrt((l_(B))/(l_(A)))`
`implies (2f_(B))/(f_(B)) = sqrt((l_(B))/(l_(A)))`
`implies 4 = (l_(B))/(l_(A))`
`implies l_(A) = (l_(B))/(4)`
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