The frequency of a vibrating air column in a pipe,open at both ends,is $f_1$. When $\frac{3}{4}$ of its length is immersed in water,the frequency of the vibrating air column is $f_2$. The value of $\frac{f_1}{f_2}$ is

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed organ pipe $L$ metre long. The length of the open pipe will be:

In a resonance tube experiment,the first and second resonance are heard when the water level is $24.1 \ cm$ and $74.1 \ cm$ respectively,below the open end of the tube. The inner diameter of the tube is (in $cm$)

At a temperature of $27^{\circ} C$, two identical organ pipes produce notes of frequency $140 \,Hz$. If the temperature of one pipe is raised to $57.75^{\circ} C$, then the number of beats produced per second is

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube,the first resonance is observed when the air column has a length of $20.0 \,cm$ for a tuning fork of frequency $400 \,Hz$. The velocity of sound at room temperature is $336 \,ms^{-1}$. The third resonance is observed when the air column has a length of ......... $cm$.

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