While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of `18 cm` during winter. Repeating the same experiment during summer, she measures the column length to be `x cm` for the second resonance. Then

Options

A. `18 gt x`
B. `x gt 54`
C. `54 gt x gt 36`
D. `36 gt x gt 18`

Answer

B

Explanation

Here, `l_(1)=18" cm"`
`f_(1)=(v_(1))/(4l_(1))impliesf_(2)=(3v_(2))/(4l_(2))`
where `l_(2)=x` according to given situation and also `v_(1)lt v_(2)` during summer temperature would be higher.
Now, `(3v_(2))/(4l_(2))=(v_(1))/(4l_(1))`
or, `" "l_(2)=3l_(1)xx(v_(2))/(v_(1))`
or, `" "x=54x`
(A quantity greater than 1)
So, `x gt 54`