In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter `5 cm` is used . The column in pipe resonates with a tuning fork of frequency `480 H_(Z)` when the minimum length of the air column is `16 cm` . Find the speed in air column at room temperature.

Explanation

(a) `D = 5 cm`

`(lambda)/(4) = l + e = l + 0.6r = l + 0.3 D`
`lambda = 4(l + 0.3D) = 4(16 + 0.3 xx 5)`
`= 70 cm = 0.7 m`
`v = f lambda = 480 xx 0.7 = 336 m//s`
(b)
`(lambda)/(2) = l + 2e rArr lambda = (v)/(f) = (320)/(320) = 1 m = 100 cm`
`lambda = 2(l + 2e)`
`100 = 2(48 + 2e) rArr e = 1cm`
`0.6r = 0.3D = 1 rArr D = 10//3 cm = 3.33 cm`
For closed pipe
`(lambda)/(4) = l + e = 48 + 1 = 49`
`lambda = 196 cm = 1.96 m`
`v = f lambda = rArr f = (v)/(lambda) = (320)/(1.96) = 163.3 Hz`