Question

A 30.0-cm-long wire having a mass of 10.0 g is fixed at the two ends and is vibrated in its fundamental mode.A 50.0-cm-long closed organ pipe, placed with its open end near the wire, is set up into resonance in its fundamental mode by the vibrating wire. Find the tension in the wire. Speed of sound in air `= 340 m s^-1`.

Answer 1

Correct Answer - C::D
Given `m=10gm`
`=10xx10^-3kg`
`I=30cm=0.3m`
Let the tension in the string will be =T
`m=Mass/(Unit length)`
`=33x10^-3 kg/m`
The fuN/Admental frequency
`rarr n_0=1/(2L) sqrt(T/m)`………..1
`rarr n_0=(v/(4I))`
`=340/(2xx30xx10^-2)`
`=170Hz`.........2
`According to equation 1 and 2 we get
`170=1/(2xx30xx10^-2)xxT/(33x10^-3)`
`rarr T=347Newtons`