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When a string is divided into three segm...

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

A

`f_(0) = f_(1) + f_(2) + f_(3)`

B

`1/f_(0) = 1/f_(1) + 1/f_(2) + 1/f_(3)`

C

`1/sqrtf_(0) = 1/sqrtf_(1) + 1/sqrtf_(2) = 1/sqrtf_(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f prop 1/l rArr l = k/f`
Now, `l=l_(1)+l_(2)+l_(3)`
`:. k/f_(0) = k/f_(1) + k/f_(2) + k/f_(3)`
`:. 1/f_(0) = 1/f_(1) + 1/f_(2) + 1/f_(3)` .
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