$A$ pipe open at both ends and a pipe closed at one end have the same length and both are vibrating in their fundamental mode. If the air column vibrating in the open pipe has a resonance frequency $n_1$ and the air column vibrating in the closed pipe has a resonance frequency $n_2$,then:

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

$A$ pipe open at both ends has a length of $1 \,m$. The air column in the pipe cannot resonate for which of the following frequencies (in $\,Hz$)? (Neglect end correction, speed of sound in air $= 340 \,m/s$)

In a resonance tube experiment,when the tube is filled with water up to a height of $17.0 \, cm$ from the bottom,it resonates with a given tuning fork. When the water level is raised,the next resonance with the same tuning fork occurs at a height of $24.5 \, cm$. If the velocity of sound in air is $330 \, m/s$,the tuning fork frequency is $...... \, Hz$.

An air column,closed at one end and open at the other,resonates with a tuning fork when the smallest length of the column is $50\, cm$. The next larger length of the column resonating with the same tuning fork is .... $cm$.

$A$ student determines the velocity of sound with the help of a closed organ pipe. If the observed length for the fundamental frequency is $24.7 \, cm$,the length for the third harmonic will be .... $cm$.