A cylinder of length `1m` is divided by a thin perfectly flexible diaphragm in the middle. It is closed by similar flexible diaphragams at the ends. The two chambers into which it is divided contain hydrogen and oxygen. The two diaphragms are set in vibrations of same frequency. What is the minimum frequency of these diaphragms for which the middle diaphragm will be motionless? Velocity of sound in hydrogen is `1100 m//s` and that in oxygen is `300 m//s`.

Answer

A

Explanation

Let `n_(1)` harmonic of the chamber containing `H_(2)` is equal to `n_(2)` harmonic of the chamber containing `O_(2)`. Then,

`n_1(nu_(H_2)/(4l)) = n_(2)(nu_(0_2)/(4l))`
`:. (n_(1))/(n_(2)) = nu_(0_2)/(4l) = (300)/(1100) = (3)/(11)`
`:. f_(min) = 3(nu_(H_2)/(4l)) = 3((1100)/(4 xx 0.5))`
`= 1650 H_(Z)`