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(D) The fundamental frequency of an organ pipe is given by $f = \frac{v}{2L}$ (for open pipe) or $f = \frac{v}{4L}$ (for closed pipe).In both cases,$f

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Both $(B)$ and $(C)$.

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(D) The fundamental frequency of an organ pipe is given by $f = \frac{v}{2L}$ (for open pipe) or $f = \frac{v}{4L}$ (for closed pipe).In both cases,$f \propto v$,where $v$ is the speed of sound in the gas.The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma RT}{M}}$,where $M$ is the molar mass of the gas.Since $T$ is constant,$v \propto \frac{1}{\sqrt{M}}$. Thus,$f \propto \frac{1}{\sqrt{M}}$.$(A)$ $M(H_2) = 2$,$M(O_2) = 32$. Since $M$ increases,$f$ decreases. Statement $(A)$ is incorrect.$(B)$ $M(O_2) = 32$,$M(N_2) = 28$. Since $M$ decreases,$f$ increases. Statement $(B)$ is correct.$(C)$ $M(He) = 4$,$M(CH_4) = 16$. Since $M$ increases,$f$ decreases. Statement $(C)$ is correct.Therefore,both $(B)$ and $(C)$ are correct.

$A$ gas is filled in an organ pipe and it is sounded in its fundamental mode. Choose the correct statement$(s)$ : ($T$ = constant)

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