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

Answer

B

Explanation

Let V and V' be the speeds of sound of sound in winter and summer respectively and f be the frequency of the tuning fork.
` :' ` For the first resonance in winter , ` f = V/(4L)` ltbgt and for the second resonance ` f = (3V')/(4K)`
` :. V/(4L) = (3V')/(4x)`
`:. x = 3L ((V')/V) = 3 xx 18 ((V')/V) = 54 ((V')/V)`
but `V' gt V` ( because speed of sound increases in summer as T is increased)
` :. x gt 54` (b) is the correct choice.