Two similar open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second when sounded together. The velocity of sound in air is ........ $m/s$.

The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is

$A$ pipe of length $1.5\ m$ closed at one end is filled with gas and resonates in its fundamental mode with a tuning fork. Another open organ pipe of same dimensions filled with air resonates in its fundamental mode with the same tuning fork. If the experiment is performed at $30\,^{\circ}C$ (speed of sound in air is $360\ m/s$ at $30\,^{\circ}C$),the speed of sound at $0\,^{\circ}C$ in the gas is ...... $m/s$ (Neglect end correction).

In the resonance tube experiment,the first resonant length is $l_1$ and the second resonant length is $l_2$. Then,the third resonant length will be:

The frequency of the fundamental tone in an open organ pipe of length $0.48 \ m$ is $320 \ Hz$. The speed of sound is $320 \ m/s$. What will be the frequency of the fundamental tone in a closed organ pipe of the same length?

Explain the formation of stationary waves in a closed pipe and derive the equations for natural frequencies (normal modes).