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 measure the column length to be x cm for the second resonance. Then

Options

A. `18gtx`
B. `xgt54`
C. `54gtxgt36`
D. `36gtxgt18`

Answer

B

Explanation

If `f= 3v_(2)//4l_(2)`, where `l_(2) = x` according to the given situation and `v_(1) lt v_(2)` as during summer, temperature would be higher, then
`(3V_(2))/(4L_(2))=(V_(1))/(4L_(2)) rArr l_(2)= 3l_(2) xx (v_(2))/(v_(1)) rArr x = 54 xx` (a quantity greater than 1)