Four open organ pipes of different lengths and different gases at same temperature as shown in figur

Question

Four open organ pipes of different lengths and different gases at same temperature as shown in figure. Let fA, fB, fC and fD be their fundamental frequencies then :[Take = 7/5]

Accepted Answer

Sol. v = $\sqrt{\frac{\gamma RT}{M}}$f = $\frac{v}{4L}$ ∝ $\frac{1}{L}\sqrt{\frac{\gamma}{M}}$$\gamma_{H_{2}} = \frac{7}{5}$, $\gamma_{O_{2}} = \frac{7}{5}$, $\gamma_{N_{2}} = \frac{7}{5}$ (Di–atomic)Also $\gamma_{CO_{2}} = \frac{7}{5}$ (linear Tri–atomic)

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