$A$ cylindrical tube,open at both ends,has a vibrating air column of fundamental frequency '$f$' in air. The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the vibrating air column is now:

An organ pipe open at one end is vibrating in its first overtone and is in resonance with another pipe open at both ends vibrating in its third harmonic. The ratio of the length of the two pipes is:

$A$ pipe of length $85\, cm$ is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below $1250\, Hz$. The velocity of sound in air is $340\, m/s$.

In the fundamental mode,the time required for a sound wave to reach the closed end of an air-filled pipe is $t$ seconds. What is the frequency of vibration of the air column?

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic)

For a certain organ pipe, three successive resonance frequencies are observed at $425 \,Hz$, $595 \,Hz$, and $765 \,Hz$, respectively. The length of the pipe is (speed of sound in air $= 340 \,m/s$). (in $\,m$)