A tuning fork of frequency `340 Hz` is excited and held above a cylindrical tube of length `120 cm`. It is slowly filled with water. The minimum height of water column required for resonance to be first heard( Velocity of sound `=340 ms^-1`) is.

Explanation

In a closed tube, the first resonance takes place, when the length of air column = `(lambda//4)`
The wavelength ofsound in air
`lambda = (v)/(n) = (340)/(340)`
= 1 m [As v = 340 m/s and n = 340]
Here length offirst resonance can be given as
`(lambda)/(4) = 0.25m`
= 25 cm
The length ofsecond resonance
`(3lambda)/(4) = (3)/(4)m`
= 75cm
The length ofthird resonance
`(5lambda)/(4) = (5)/(4)`
= 125 cm
As the length ofthe tube is only 120 cm, hence third resonance is not possible.
Therefore, the minimum height ofwater required for resonance
= 120 - 75 = 45 cm