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 tunning fork is `0.1m` . When this length is changed to `0.35m`, the same tunning fork resonates with the first overtone. calculate the end correction.
(a) `0.012 m`
(b) `0.025 m`
( c) `0.05 m`
(d) `0.024 m`

Options

A. `0.012 m`
B. `0.025 m`
C. `0.05 m`
D. `0.024 m`

Answer

B

Explanation

`l_(1) + x = (lamda)/(4) rArr lamda = 4(l_(1) + x)`
`(l_(2) + x) = (3 lamda)/(4) rArr lamda = (4)/(3) (l_(2) + x)`
`:. v_(1) = (v)/(lamda_(1) = (v)/(4(l_(1) + x))`
`:. v_(2) = (v)/(lamda_(2)) = (3v)/(4(l_(2) + x))`
Given `v_(1) = v_(2)`
`rArr (v)/(4(l_(1) +x))=(3v)/(4(l_(2)+x)) rArr x = 0.025 m`.