Three similar wires of frequency `n_(1),n_(2)` and `n_(3)` are joined to make one wire. Its frequency will be

Options

A. `n=n_(1)+n_(2)+n_(3)`
B. `(1)/(n)=(1)/(n_(1))+(1)/(n_(2))+(1)/(n_(3))`
C. `(1)/(sqrt(n))=(1)/(sqrt(n_(1)))+(1)/(sqrt(n_(2)))+(1)/(sqrt(n_(3)))`
D. `(1)/(n^(1))=(1)/(n_(1)^(2))+(1)/(n_(2)^(2))+(1)/(n_(3)^(2))`

Answer

B

Explanation

Frequency `(f)=(1)/(2l)sqrt((T)/(mu))`
`implies f_(1)l_(1)=f_(2)l_(2)=f_(3)l_(3)=k`
Now, `l_(1)+l_(2)+l_(3)=limplies(k)/(f_(1))+(k)/(f_(2))+(k)/(f_(3))=(k)/(f)`
`implies (1)/(f)=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3))implies(1)/(n)=(1)/(n_(1))+(1)/(n_(2))+(1)/(n_(3))`.