The frequency of a stetched unifrom wire under tension is in resonance with the fundamental frequency of closed tube. If the tension in the wire is increased by 8 N, it is in resonance with the first overtone of the closed tube. The initial tension in the wire is

Options

A. 1 N
B. 4 N
C. 8 N
D. 16 N

Answer

A

Explanation

Frequency of strectched string `n=1/(2l)sqrt(T/m)`
Fundamental frequency of closed tube ,`n_2=v/(4l)`
Fundamental frequency of first overtone of closed tube,`n_3=3v/(4l)`
According to `1^(st)` condition, `n_1=n_2`
`1/(2l)sqrt(T/m)=v/(4l)` (1)
`1/(2l)sqrt((T+8)/m)=(3v)/(4l)` (2)
Dividing equation (1) by equation (2),
`sqrt(T/m)/sqrt((T+8)/m)=1/3`
`T/mxxm/(T+8)=1/9`
`9T=T+8`
`implies 8T=8`
`:. T=1N`