While measuring the speed of sound by performing a resonace column experiment, a student gets the first resonance condition at a column length of `18 cm` during winter. Repeating the same experiment during summer, the resonance. Then

Options

A. (a) `18 gt x`
B. (b) `x gt 54`
C. (c ) `54 gt x gt 36`
D. (d) `36 gt x gt 18`

Answer

B

Explanation

(b) For first resonant length `v = (v)/(4l_(1)) = (v)/(4 xx 18)` (in water)
For second resonant length
`v' = (3v')/(4l_(2)) = (3v')/(4x)` (in summer) :. `(v)/((4 xx 18) = (3v')/(4 xx x)`
:. `x = 3 xx 18 xx (v')/(v)` :. `x = 54 xx (v')/(v)cm`
`v'gt v` because velocity of light is greater in summer as compared ti winer `(v prop sqrt(T))`
:. `x gt 54 cm`