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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 ` v_(1) , v_(2) and v_(3)` respectively .
The original fundamental frequency (v) of the string is

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_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
Let l be the length of the string .
Fundamental frequency is given by ` v = (1)/(2l) sqrt((T)/(mu))`
or , `v prop (1)/(l)` [ `:. T and mu ` are constant ]
or , `v = (k)/(l)` , where k is a constant
Here, `l_(1) = (k)/(v_(1)), l_(2) =(k)/(v_(2)), l_(3) = (k)/(v_(3)) and l= (k)/(v)`
`:. (1)/(v) = (1)/(v_(1)) + (1)/(v_(2)) + (1)/(v_(3)) ` [ ` :. l = l_(1) + l_(2) + l_(3)` ]
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