How many degrees of freedom the gas molecules have if, under \(\text{STP}\), the gas density \(\rho = 1.3~\text{kg/m}^3\) and the velocity of sound propagation in it is \(330~\text{ms}^{-1}\)${\mathrm{}}^{}$?
1. \(3\)       
2. \(5\)         
3. \(7\)             
4. \(8\)

The isothermal elasticity of a medium is ${\mathrm{E}}_{\mathrm{i}}$ and the adiabatic elasticity in ${\mathrm{E}}_{\mathrm{a}}$. The velocity of sound in the medium is proportional to

1.  ${\mathrm{E}}_{\mathrm{i}}$

2.  ${\mathrm{E}}_{\mathrm{a}}$

3.  $\sqrt{{\mathrm{E}}_{\mathrm{i}}}$

4.  $\sqrt{{\mathrm{E}}_{\mathrm{a}}}$

The equation of plane progressive wave motion is y=a sin 2$\mathrm{\pi }/\mathrm{\lambda }$(vt-x). Velocity of particle is

1. $y\frac{dv}{dx}$

2. $v\frac{dy}{dx}$

3. $-y\frac{dv}{dx}$

4. $-v\frac{dy}{dx}$

A person speaking normally produces a sound of intensity 40 dB at a distance of 1 m. If threshold intensity fo r reasonable audibility is 20 dB, the maximum distance at which he can be heared clearly is:

1. 4 m

2. 5 m

3. 10 m

4. 20 m

The equation of a simple harmonic wave is given by 

          $\mathrm{y}=3 \sin \frac{\mathrm{\pi }}{2}(50\mathrm{t}-\mathrm{x})$

where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

1. $2\mathrm{\pi }$

2. $\frac{3}{2}\mathrm{\pi }$

3. $3\mathrm{\pi }$

4. $\frac{2}{3}\mathrm{\pi }$