Consider a gas with molar mass $M$. If sound at frequency $f$ is introduced to a tube of this gas at temperature $T$, an internal acoustic standing wave is set up with nodes separated by $L$. The adiabatic constant $\gamma = \frac{C_p}{C_v}$ is

In the experiment for the determination of the speed of sound in air using the resonance column method,the length of the air column that resonates in the fundamental mode with a tuning fork is $0.1 \ m$. When this length is changed to $0.35 \ m$,the same tuning fork resonates with the first overtone. Calculate the end correction in $m$.

$A$ closed organ pipe of length $L_1$ and an open organ pipe contain diatomic gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibilities of the gases are same in both pipes,which are vibrating in their first overtone with the same frequency. The length of the open organ pipe is (Neglect end correction).

In the experiment to determine the speed of sound using a resonance column, which of the following statements is correct?

$A$ student is performing an experiment using a resonance column and a tuning fork of frequency $244 \ s^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350 \pm 0.005) \ m$,the gas in the tube is. (Useful information: $\sqrt{167 RT} = 640 \ J^{1/2} \ mol^{-1/2}$; $\sqrt{140 RT} = 590 \ J^{1/2} \ mol^{-1/2}$. The molar masses $M$ in grams are given in the options. Take the value of $\sqrt{\frac{10}{M}}$ for each gas as given there.)

$A$ closed organ pipe and an open organ pipe are filled with two different gases having the same bulk modulus but different densities $\rho_1$ and $\rho_2$ respectively. The frequency of the $9^{\text{th}}$ harmonic of the closed pipe is identical to the $4^{\text{th}}$ harmonic of the open pipe. If the length of the closed pipe is $10 \ cm$ and the density ratio of the gases is $\rho_1 : \rho_2 = 1 : 16$,then the length of the open pipe is: