In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is `0.1m`. When this length is changed to `0.35m`, the same tuning fork resonates with the first overtone. Calculate the end correction.

Options

A. `0.05 m`
B. `0.012 m`
C. `0.018 m`
D. `0.025 m`

Answer

D

Explanation

Given :
Initial length of air-column `(l_(1)) = 0.1 m` and final length of air-column `(l_(2)) = 0.35 m`. We know that frequnency of fundamental mode
`(v_(1)) = (v)/(4(l_(1) + e)) = (v)/(40(0.1+e)) "….."(i)`
Similarly, frequency of first overtone
`(v_(2)) = (3v)/(4(l_(2) + e)) = (3v)/(4(0.35 +e)) "....."(ii)`
Since these frequencies are equal, therefore
`(v)/(4(0.1+e)) = (3v)/(4(0.35)+e)`
or `0.35 + e = 0.3 + 3e`
or `2e = 0.35 - 0.3 = 0.05`
or `e = 0.025 m`
(Where `e=` End correction of air column)