An open organ pipe of length $l$ is sounded together with another organ pipe of length $l + x$ in their fundamental tones $(x << l)$. The beat frequency heard will be (speed of sound is $v$):

In the fundamental mode, the time required for a sound wave to reach the closed end of a pipe filled with air is $t$ seconds. What is the frequency of vibration of the air column? ($\lambda$ = wavelength of the wave)

$A$ tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27\,^{\circ}C$,two successive resonances are produced at $20\,cm$ and $73\,cm$ of column length. If the frequency of the tuning fork is $320\,Hz$,the velocity of sound in air at $27\,^{\circ}C$ is .... $m/s$.

The first resonance length of a resonance tube is $40\, cm$ and the second resonance length is $122\, cm$. The third resonance length of the tube will be... $cm$

The length of an open organ pipe is twice the length of a closed organ pipe. The fundamental frequency of the open pipe is $100 \ Hz$. The frequency of the third harmonic of the closed pipe is: (in $Hz$)

The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is $100 \ Hz$. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is: (in $Hz$)