A `3.6m` long vertical pipe resonates with a source of frequency `212.5 Hz` when water level is at certain height in the pipe. Find the height of water level (from the bottom of the pipe) at which resonance occurs. Neglect end correction. Now , the pipe is filled to a height `H (~~ 3.6m)`. A small hole is drilled very close to its bottom and water is allowed to leak. Obtain an expression for the rate of fall of water level in the pipe as a function of `H`. If the radii of the pipe and the hole are `2 xx 10^(-2)m` and `1 xx 10^(-3)m` respectively, calculate the time interval between the occurance of first two resonances. Speed of sound in air `340m//s` and `g = 10m//s^(2)`.

Answer

A, B, C, D

Explanation

Speed of sound, `v = 340m//s`.
Let `l_(0)` be the length of air column corresponding to the fundamental frequency. Then
`(v)/(4l) = 212.5`
or `l_(0) = (v)/(4(212.5)) = (340)/(4(212.5)) = 0.4m`