Question

The air in a closed tube `34 cm` long is vibrating with two nodes and two antinodes and its temprature is `51^(@)C`. What is the wavelength of the waves produced in air outside the tube, when the temperature of air is `16^(@)C`?
A. `42.8 cm`
B. `68 cm`
C. `17 cm`
D. `102 cm`

Answer 1

Correct Answer - A
`l = (3 lambda)/(4)`
`:. lambda = (4l)/(3) = (4(34))/(3) = 45.33 cm`
`lambda = (nu)/(f)`
`lambda prop nu` (as `f =`constant)
and `nu prop sqrt(T)` `(T =` temperature)
`:. lambda prop sqrt(T)`
`:. (lambda_(2))/(lambda_(1)) = sqrt((T_(2))/(T_(1))`
`:. lambda_(2) = (sqrt((T_(2))/(T_(1)))) lambda_(1)`
`=(sqrt((16 xx 273)/(51 xx 273))) (45.33)`
`= 42.8 cm`