\(4.0~\text{gm}\) 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 n₁, n_2, and n₃ 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=$340$ $m/s$) 

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 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of 513 Hz. The unknown frequency will be:

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

$1.$ $y=\sin \left(2\pi x-2\pi t\right)$

$2.$ $y=\sin \left(10\pi x-20\pi t\right)$

$3.$ $y=\sin \left(2\pi x+2\pi t\right)$

$4.$ $y=\sin \left(x-2t\right)$