An air column closed at one end and opened at the other end , resonates with a tuning fork of frequency `v` when its length is `45 cm` and `99 cm` and at two other lengths in between these values. The wavelength of sound in air column is

Options

A. `180 cm`
B. `108 cm`
C. `54 cm`
D. `36 cm`

Answer

D

Explanation

`45 cm = 5 ( 9 cm)` and `99 cm = 11 ( 9 cm)`
So two other lengths between these two values are `7 ( 9 cm) and 9 ( 9 cm)` , i.e., `63 cm and 81 cm` respectively .
So the fundamental length is `9 cm`
`9 = (lambda)/(4) ` ( for a closed organ pipe)
`lambda = 36 cm`