The ratio of the frequencies of the fundamental harmonic produced by an open pipe to that of a closed pipe having the same length is

$A$ closed organ pipe of length $l$ is sounded together with another closed organ pipe of length $l + x$ $(x << l)$,both in their fundamental mode. If $v$ is the speed of sound,the beat frequency heard is:

In a resonance tube experiment,the first resonance is obtained for $10\, cm$ of air column and the second for $32\, cm$. The end correction for this apparatus is ....$cm$

When the air column of a resonance tube is vibrated together with a tuning fork,$3$ beats are heard per second,either the temperature of the air column is $51^{\circ} C$ or $16^{\circ} C$. The frequency of the tuning fork is (in $Hz$)

The fundamental frequency of an air column in a pipe open at both ends is $f_1$. Now $80\%$ of its length is immersed in water,the fundamental frequency of the air column becomes $f_2$. The ratio of $f_1:f_2$ is

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 $Hz$)