A closed orgain pipe of length `l_(0)` is resonating in `5^(th)` harmonic mode with rod clamped at two points `l` and `3l` from one end. If the length of the rod is `4l` and it is vibrating in first overtone. Find the length of the rod. [Velocity of sound in air `=v_(s)` Young's modulus for the rod `Y` and density `rho`]

Explanation

For section `AB`
`f=(5v_(s))/(4l_(0))=(V_(rod))/(lambda)`
Where, `l=(lambda)/(4)+(lambda)/(2)=(3lambda)/(4)`
` :. 4l=3lambda`
`:. "Length of rod" 4l=3lambda`
`=3xx(4l_(0)V_(rod))/(5V_(s))`
`=(12rho_(0)V_(rod))/(5V_(s))`