The fundamental frequency of a closed pipe is $400 \,Hz$. If $1/3$ of the pipe is filled with water,the frequency of the $2^{\text{nd}}$ harmonic of the pipe will be (Neglect end correction). (in $\,Hz$)

$A$ closed organ pipe has a fundamental frequency $n$. If its length is doubled and its radius is halved,its frequency nearly becomes

$A$ 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).

For air at room temperature, the atmospheric pressure is $1.0 \times 10^{5} \text{ Nm}^{-2}$ and the density of air is $1.2 \text{ kgm}^{-3}$. For a tube of length $1.0 \text{ m}$, closed at one end, the lowest frequency generated is $84 \text{ Hz}$. The value of $\gamma$ (ratio of two specific heats) for air is:

What should be the length of a closed pipe to produce resonance with a sound wave of wavelength $62 \,cm$,in fundamental mode (in $\,cm$)? [Neglect end correction]

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequency of the new pipe is