A string `25 cm` long and having a mass of `2.5 g` is under tension. A pipe closed at one end is `40 cm` 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 tencion in the string decrease the beat frequency. If the speed of sound in air is `320 m//s`, find the tension in the string.

Explanation

`mu = (2.5)/(25) = 0.1 g // cm = 10^(-2) Kg//m`
`1^(st)` overtone

`lambda_(s) = 25 cm = 0.25 m rArr f_(s) = (1)/(lambda_(s)) sqrt((T)/(mu))`
pipe is fundamental freq
`lambda_(p) = 160 cm = 1.6 m rArr f_(p) = (V)/(lambda_(p))`

`:'` by decreasing the tension, beat freq is decreased
`:. f_(s) lt f_(p) rArr f_(s) - f_(p) = 8 rArr (1)/(0.25) sqrt((T)/(10^(-2))) - (320)/(1.6) = 8 rArr T = 27.04 N`