AB is a cylinder of length 1 m fitted with a thin flexible diaphragm C at the middle and two other thin flexible diaphragm at ends A and B which do not allow outside air to mix with H2 and O2 gas as shown. Find the minimum frequency of a tuning fork which can establish sustained stationary waves in cylinder with diaphragm C as a node. Given that velocity of sound in H2 is 1100 m/s and in O2, is 300 m/s.

For sustained stationary wave in both gas, independently stationary wave must setup in  H2 & in O2Resonating frequency of stationary wave formation in H2 is nH2=(2n+1)vH24lResonating frequency of stationary wave formation in O2 is nO2=(2m+1)vO24lfor stationary wave to be produced in both gases we use nH2=nO2(2n+1)vn24l=(2m+1)vα24l⇒2m+12n+1=1100300=113for min  frequency 2m+1=11 2n+1=3⇒nmin=3vh24l=3×11004×0.5=1650Hz