$4.0~\text{gm}$ of gas occupies $22.4~\text{litres}$ at NTP. The specific heat capacity of the gas at a constant volume is  $5.0~\text{JK}^{-1}\text{mol}^{-1}.$ If the speed of sound in the gas at NTP is $952~\text{ms}^{-1},$ then the molar heat capacity at constant pressure will be:
($R=8.31~\text{JK}^{-1}\text{mol}^{-1}$) 

The fundamental frequency of a closed organ pipe of a length $20$ cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

If $n_1$, $n_2$_, and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by:
1. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
2. $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$
3. $\sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}$
4. $n=n_1+n_2+n_3$

The number of possible natural oscillations of the air column in a pipe closed at one end of length $85$ cm whose frequencies lie below $1250$ Hz are:(velocity of sound= $340~\text{m/s}$) 
1. $4$
2. $5$
3. $7$
4. $6$

A source of unknown frequency gives $4$ beats/s when sounded with a source of known frequency of $250~\text{Hz}.$ The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of $513~\text{Hz}.$ The unknown frequency will be:

A wave traveling in the +ve $x\text-$direction having maximum displacement along $y\text-$direction as $1~\text{m}$, wavelength $2\pi~\text{m}$ and frequency of $\frac{1}{\pi}~\text{Hz}$, is represented by: