$A$ closed pipe of length $10 \, cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe is ......... $cm$.

$A$ standing wave in a pipe with a length $L=1.2 \,m$ is described by $y(x, t)=y_0 \sin [(2 \pi / L) x] \sin [(2 \pi / L) x+\pi / 4]$. Based on the above information,which one of the following statements is incorrect? (Speed of sound in air is $300 \,ms^{-1}$)

When an open pipe is closed from one end, the second overtone of the closed pipe is higher in frequency by $100 \text{ Hz}$ than the first overtone of the open pipe. The fundamental frequency of the open pipe will be (Neglect end correction). (in $\text{ Hz}$)

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

$A$ closed organ pipe of length $L_c$ and an open organ pipe of length $L_o$ contain different gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of the open organ pipe?

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]