$4.0 \text{ gm}$ of gas occupies $22.4 \text{ litres}$ at NTP. The specific heat capacity of the gas at a constant volume is $5.0 \text{ J K}^{-1}\text{mol}^{-1}$. 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: ($R=8.31 \text{ J K}^{-1}\text{mol}^{-1}$)

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

When a string is divided into three segments of lengths $l_1, l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1, \nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string is:

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

The two nearest harmonics of a tube closed at one end and open at the other end are $220 \text{ Hz}$ and $260 \text{ Hz}$. What is the fundamental frequency of the system?

A transverse wave propagating along the $x$-axis is represented by: $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \frac{\pi}{4})$, where $x$ is in meters and $t$ in seconds. The speed of the wave is:

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \text{ cm}$, the length of the open organ pipe is:

The number of possible natural oscillations of the air column in a pipe closed at one end of a length of $85 \text{ cm}$ whose frequencies lie below $1250 \text{ Hz}$ is: (velocity of sound $340 \text{ ms}^{-1}$)

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