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).

In a closed organ pipe,the frequency of the fundamental note is $30 \,Hz$. $A$ certain amount of water is now poured into the organ pipe so that the fundamental frequency increases to $110 \,Hz$. If the organ pipe has a cross-sectional area of $2 \,cm^2$,the amount of water poured into the organ tube is . . . . . . $g$. (Take the speed of sound in air as $330 \,m/s$)

An open pipe of length $33 \ cm$ resonates with a frequency of $1000 \ Hz$. If the speed of sound is $330 \ m/s$,then this frequency is:

$A$ tuning fork of frequency $480\, Hz$ is used in an experiment for measuring the speed of sound $(\nu)$ in air by the resonance tube method. Resonance is observed to occur at two successive lengths of the air column,$\ell_1 = 30\, cm$ and $\ell_2 = 70\, cm$. Then $\nu$ is equal to ..... $m/s$.

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

$A$ flute,which we treat as a pipe open at both ends,is $34\, cm$ long. The fundamental frequency of the flute when all its holes are covered is .... $Hz$ [Take velocity of sound in air $= 340\, m/s$].