AB wire (length x) is vibrating in its fundamental mode. Wire AB is in resonance with resonance tube in which air column (length x/2) is also vibrating with its fundamental mode. Sound speed is 400 m/sec and linear mass density of AB wire is `10^-4` kg/m and g=10 `m//sec^2`, value of mass m =`[beta(10^-1)] kg`, then find value of `beta`.Neglect the masses of wires in comparison to block's mass 'm'.

Explanation

`T_1=2T_0=2[(2m(2m))/(m+2m)]g`
`T_1=(8m)/3g=(80m)/3`...(i)
In resonance ,
`f_(wire)=f_(tube)`
`((1)V_1)/(2l_1)=((1)V_2)/(4l_2)`
`((sqrt(T_1/mu)))/(2(x))=((400))/(4(x/2))`
`rArr T_1=mu(16xx10^4)`
From (i), `80/3m=10^-4(16xx10^4)`
`m=0.6 kg.`