Four open organ pipes of different lengths and different gases at same temperature are as shown in figure. Let  $f_A,f_B,f_c\text{ and }{f}_D$ be their fundamental frequencies then : 
[Take  ${\gamma }_{C{O}_2}=7/5$ ]

$f=\frac{v}{2L}=\frac{\sqrt{\frac{\gamma RT}{M}}}{2L}=\frac{\sqrt{\frac{\gamma }{M}\times k}}{2L}$

For pipe $A\left({\mathrm{H}}_2\right),$ 

$\therefore F_A=\frac{\sqrt{\frac{7}{5\times 2}} k}{2L}=\frac{\sqrt{7}k}{2\sqrt{10}L}$

For pipe $B\left(O_2\right),$

$\therefore F_{\mathrm{B}}=\frac{\sqrt{\frac{7}{5\times 32}}k}{2L}=\frac{\sqrt{7}k}{2\sqrt{160}\frac{L}{2}}=\frac{\sqrt{7}k}{\sqrt{160}L}$

For pipe $C\left({ \mathrm{N}}_2\right),$

$\therefore F_{\mathrm{C}}=\frac{\sqrt{\frac{7}{5\times 28}}k}{2L}=\frac{\sqrt{7}k}{2\sqrt{140}\frac{2L}{3}}=\frac{3k}{4\sqrt{20}L}$

For pipe $D\left({\mathrm{CO}}_2\right) ,$

$\therefore F_{\mathrm{D}}=\frac{\sqrt{\frac{7}{5\times 44}}k}{2L}=\frac{\sqrt{7}k}{2\sqrt{220}\frac{L}{3}}=\frac{3\sqrt{7}k}{2\sqrt{220}L}$

$f_A/f_B=2$

$\frac{f_C}{f_D}=\sqrt{\frac{11}{28}}$

$\frac{f_B}{f_C}=\sqrt{\frac{14}{9}}$

$\frac{f_D}{f_A}=\sqrt{\frac{9}{22}}$