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

Answer

B

Explanation

For first resonant length
`v=v/(4l_1)=v/(4 times 18)` (in winter)
For second resonant length
`v.=(3v.)/(4l_2)=(3v.)/(4x)`(i n su mmer)
`thereforev/(4 times18)=(3v.)/(4 timesx)`
`therefore x=3 times 18 times v./v therefore x=54 times v./v cm`
`v. gt v` because velocity of light in summer as compared to winter `(v prop sqrtT) therefore x gt 54 cm`