The stationary wave $y = 2a \sin kx \cos \omega t$ in a closed organ pipe is the result of the superposition of $y = a \sin (\omega t - kx)$ and

$A$ glass tube of $1 \,m$ length is filled with water. The water can be drained out slowly from the bottom of the tube. If a vibrating tuning fork of frequency $500 \,Hz$ is brought at the upper end of the tube, then the total number of resonances obtained are [Velocity of sound in air is $320 \,m/s$].

In a pipe closed at one end,an air column is vibrating in its second overtone. The column has

$A$ 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).

$A$ 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 $300 \,ms^{-1}$)

$A$ pipe open at both ends of length $1.5 \ m$ is dipped in water at one end such that the $2^{\text{nd}}$ overtone of the vibrating air column is resonating with a tuning fork of frequency $330 \ Hz$. The length of the pipe immersed in water is (Speed of sound in air $= 330 \ m/s$) (Neglect end correction). (in $m$)