The end correction of a resonance column is $1 \, cm$. If the shortest length resonating with the tuning fork is $10 \, cm$,the next resonating length should be ..... $cm$.

An open organ pipe having fundamental frequency $(n)$ is in unison with a vibrating string. If the tube is dipped in water so that $75 \%$ of the length of the tube is inside the water,then the ratio of the fundamental frequency of the air column of the dipped tube to that of the string will be (Neglect end corrections).

When an open pipe is closed from one end, the third overtone of the closed pipe is higher in frequency by $150 \text{ Hz}$ than the second overtone of the open pipe. The fundamental frequency of the open pipe will be (Neglect end correction). (in $\text{ Hz}$)

$A$ pipe $60 \ cm$ long and open at both ends produces harmonics. Which harmonic mode of the pipe resonates with a $2.2 \ kHz$ source? (Speed of sound in air $= 330 \ m/s$) (Neglect end correction)

$A$ closed organ pipe and an open organ pipe of the same length produce $2 \text{ beats/second}$ while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of the closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is

$A$ pipe $P_{C}$ closed at one end and a pipe $P_{O}$ open at both ends are vibrating in their second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe $P_{C}$ to $P_{O}$ is (Neglect end correction):