In the experinment for the determinnation of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fu ndamental mode , with a tuning fork is `0.1 m` . When this length is changed to `0.35m` , the same tuning fork resonates with the first overtone. Calculate the end correction.
(a) `0.012 m`
(b) `0.0025 m`
(c) `0.05 m`
(d) `0.024 m`

Explanation

Let `e` be the end correction.
Given that, fundamental tone for a length `0.1 m` = first overtone for the length `0.35 m` .
`(upsilon)/(4(0.1 + e)) = (3 upsilon)/(4(0.35 + e))`
Solving this equation, we get `e = 0.025 m = 2.5 cm` .
`:.` The correct option is (b).
`l_(2) + e = 3 lambda//4` and `l_(1) + e = lambda//4`
Solving these two equations, we get
`e = (l_(2)-3l_(1))/(2) = (0.35 - 3xx0.1)/(2)= 0.025 m`