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 y`
B. `y gt 54`
C. `54 gt y gt 36`
D. `36 gt y gt 18`

Answer

B

Explanation

Let `upsilon` be the velocity of sound.
For first resonance occurring at x = 18 cm, `upsilon_(1)` is the speed of sound in winter.
`f = (upsilon_(1))/(4x) = (upsilon_(1))/(4 xx (0.18)) = (upsilon_(1))/(0.72)`
For second resonance occurring at y, `upsilon_(2)` is the speed of sound in summer.
`f' = (3 upsilon_(2))/(4y)" "(because upsilon_("sound") = sqrt((gamma RT)/(M)))`
f = f'
`therefore" "(upsilon_(1))/(4 xx (0.18)) = (3 upsilon_(2))/(4y)`
`y = 0.54 ((upsilon_(2))/(upsilon_(1)))`
`y gt 54` cm