An open organ pipe and a closed organ pipe of the same length $L$ produce $2$ beats per second when they are set into vibrations together in their fundamental modes. The length of the open pipe is made half and that of the closed pipe is doubled. The number of beats produced per second will be (neglect end correction).

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 $...... \, Hz$.

If in an experiment for determination of velocity of sound by resonance tube method using a tuning fork of $512 \ Hz$,the first resonance was observed at $30.7 \ cm$ and the second was obtained at $63.2 \ cm$,then the maximum possible error in the velocity of sound is ..... $cm/s$ (consider the actual speed of sound in air is $332 \ m/s$).

In a resonance tube,the first resonance is obtained when the level of water in the tube is at $16\,cm$ from the open end. Neglecting end correction,the next resonance will be obtained when the level of water from the open end is .... $cm$

$A$ cylindrical tube open at both ends has a fundamental frequency $f$ in air. When the tube is dipped vertically in water so that one-third part of the tube is in water,the fundamental frequency of the air column becomes (neglect end correction).

$A$ pipe open at both ends produces a fundamental frequency $n_1$. When the pipe is kept with $\frac{3}{4}$ of its length in water,it produces a note of fundamental frequency $n_2$. The ratio of $\frac{n_1}{n_2}$ is