Six antinodes are observed in the air column when a standing wave forms in a Kundt's tube . What is the length of the air column if steel bar of ` 1 m` length is clamped at the middle .
The velocity of sound in steel is `5250 m//s` and in air `343 m//s`.

Answer

`39.2 cm`

Explanation

Kundt's tube is a closed organ pipe . Nodes are formed at ends . The separartion between six antinodes is `5 lambda//2`.
`= (lambda)/(4) + ( 5lambda)/(2) + (lambda)/(4) = 3 lambda`
If steel rod is clamped in the middle , node is formed in the middle and antinodes at ends.
`:. l_(steel) = (lambda_(steel))/( 2)`
or `lambda_(steel) = 2 l_(steel) = 2 m`
Also ` n_(air) = n_(steel)`
`:. (v_(air))/(lambda_(air)) = (v_(steel))/( lambda_(steel))`
`lambda_(air) = (v_(air))/(v_(steel)) xx lambda_(steel)`
` = (343)/(5250) xx 2 = 0.1306 m`
`:. l_(air) = 3 lambda_(air) = 3 xx 0.1306 = 39.2 cm`