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.

Answer

`27.04 N`

Explanation

`F_("string") gt F_("pipe")`
`F_("string")=(2)/(2L)sqrt((T)/(mu))=4sqrt((T)/(10^(-2)))=40sqrt(T)`
`F_("pipe")=(v)/(lamda)=(320)/(4xx0.4)=200Hz`
`rArr 40 sqrt(T)=200=8rArr T=27.04N`