A string `25cm` long and having a mass of `2.5 gm` is under tension. A pipe closed at one end is `40cm` long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, `8` beats per second are heard. It is observed that decreasing the tension in the string decreases beat frequency. If the speed of sound in air is `320m//s`, find the tension in the string.

Options

A. `27N`
B. `54N`
C. `13.5N`
D. `108N`

Answer

D

Explanation

`n_(s)=(1)/(2l_(s))sqrt((T)/(mu))`, `n_(c )=(V)/(4L_(c ))=(320)/(4xx40xx10^(-2))`
`impliesn_(c )=200Hz`, `Deltan=n_(s)~n_(c )`, `Deltan. lt Deltan` as ` n prop sqrt(T)impliesn. ltn` as `T. lt T` this is possible when `n_(s)-n_(c )=Deltan`, `n_(s)=200+8=208Hz`