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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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Knowledge Check

  • If n_1, n_2 and n_3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

    A
    `1/n=1/n_1+1/n_2=1/n_3`
    B
    `1/sqrtn=1/sqrtn_1+1/sqrtn_2+1/sqrtn_3`
    C
    `sqrtn=sqrtn_1+sqrtn_2+sqrtn_3`
    D
    `n=n_1+n_2+n_3`

  • The length of a wire is l_1 when tension is T_1 and l_2 when tension is T_2 . The original length of the wire is

    A
    `(l_1+l_2)/2`
    B
    `(l_1T_2+l_2T_1)/(T_1+T_2)`
    C
    `(l_1T_2-l_2T_1)/(T_1-T_2)`
    D
    `(l_1T_2+l_2T_1)/(T_1+T_2)`

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