The glass tube of a resonance tube apparatus is held vertically and the length of the air column in it can be adjusted by adjusting the water level in the tube using a pipe and funnel arrangement. A tuning fork, of frequency v is sounded above the air column in the tube while the length of the air column is slowly increased, starting with a small value. whenever resonance occurs, it is indicated by a loud sound. the two successive lengths at which resonance occurs are `l_(1) and l_(2)`. find the speed of sound in air and the end correction for this pipe.

Explanation

let the end correction be e. the results of the experiment just described have been summarised in the figure below.
Now `l_(1)=e=(lamda)/(4)` . . . (i)
and `l_(2)=e=(3lamda)/(4)` . . . (ii)
Subtracting (i) and (ii), we get
`l_(2)-l_(1)=(lamda)/(2)`
or `lamda=2(l_(2)-l_(1))` . . . (iii)
Hence, the speed of sound v, is given by
`V=vlamda`
or `V=2v(l_(2)-l_(1))`
From (i) and (iii), we have
`l_(1)+e=(lamda)/(4)=(2(l_(2)-l_(1)))/(4)`
or `e=(l_(2)-3l_(1))/(2)`