\(4.0~\text{gm}\) 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:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\)) 

A string is stretched between fixed points separated by \(75.0~\text{cm}\). It is observed to have resonant frequencies of \(420~\text{Hz}\) and \(315~\text{Hz}\). There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
1. \( 155 \mathrm{~Hz} \)
2. \( 205 \mathrm{~Hz} \)
3. \( 10.5 \mathrm{~Hz} \)
4. \( 105 \mathrm{~Hz}\)

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= $\mathrm{}$\(340~\text{m/s}\)) 
1. \(4\)
2. \(5\)
3. \(7\)
4. \(6\)

If we study the vibration of a pipe open at both ends, then which of the following statements is not true:

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 \(x\)-direction having maximum displacement along \(y\)-direction as \(1~\text{m}\), wavelength \(2\pi ~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
1. \(y=\sin (2 \pi x-2 \pi t)\)
2. \(y=\sin (10 \pi x-20 \pi t)\)
3. \(y=\sin (2 \pi x+2 \pi t)\)
4. \( y=\sin (x-2 t)\)