Sound WavesHardBloom L3
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]
Options
A.fC/fD = $\sqrt{\frac{11}{28}}$ (D) fD/fA =$\sqrt{\frac{76}{11}}$
B.fB/fC = $\sqrt{\frac{72}{28}}$
C.fC/fD = $\sqrt{\frac{11}{28}}$
D.fD/fA =$\sqrt{\frac{76}{11}}$
Solution
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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