$A$ pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to

In a physics lab,a student is performing an experiment with a resonance tube to find the speed of sound and its end correction. For this,he used a resonance tube of length $120 \ cm$. When the length of the air column in the tube is $16 \ cm$ and $50 \ cm$,he obtains the $I$ and $II$ resonance respectively,while a tuning fork of frequency $500 \ Hz$ is sounded just above the tube. Match the parameters in List-$I$ with their suitable values in List-$II$.

List-$I$	List-$II$
$A$. Wavelength of sound $(cm)$	$p$. $1$
$B$. Height of liquid column at $II$ resonance $(cm)$	$q$. $2$
$C$. Speed of sound $(m/s)$	$r$. $340$
$D$. End correction $(cm)$	$s$. $68$
$E$. Minimum level of liquid column at resonance $(cm)$	$t$. $70$

In the fundamental mode,the time required for a sound wave to reach the closed end of an air-filled pipe is $t$ seconds. What is the frequency of vibration of the air column?

The fundamental frequency of an open pipe of length $0.5 \ m$ is equal to the frequency of the first overtone of a closed pipe of length $l_c$. The value of $l_c$ in meters is:

$A$ student is performing an experiment using a resonance column and a tuning fork of frequency $244 \ s^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350 \pm 0.005) \ m$,the gas in the tube is. (Useful information: $\sqrt{167 RT} = 640 \ J^{1/2} \ mol^{-1/2}$; $\sqrt{140 RT} = 590 \ J^{1/2} \ mol^{-1/2}$. The molar masses $M$ in grams are given in the options. Take the value of $\sqrt{\frac{10}{M}}$ for each gas as given there.)

If the length of a closed organ pipe is $1 \ m$ and the velocity of sound is $330 \ m/s$,then the frequency for the second note (first overtone) is: