A string `1 m` long and having linear mass density `10 g//m` is sounded with a closed pipe of length `75 cm`. When string is vibrating in its first overtone and the air in the pipe in its fundamental frequency, `5 beats//s` are heard. It is observed that decreasing the tension in the string decreases the beat frequency. If the speed of sound in air is `315 m//s`, Find the tension in the string.

Explanation

The frequency of second overtone
`f_(2) = (2)/(2L) sqrt((T)/(mu)) = 1 sqrt((T)/(10 xx 10^(-3)))`
`= 10 sqrt(T)`

The fundamental frequency
`n = (v)/(4 l) = (315)/(4 xx 0.75) = 105 Hz`
As tension decreases, beat frequency decrease i.e.
`f_(2) gt n`
`f_(2) - n = 5`
`10 sqrt(T) - 105 = 5`
`10 sqrt(T) = 110`
`sqrt(T) = 11 rArr T = 121 N`