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

4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K^-1mol^-1. If the speed of sound in this gas at NTP is$952 m{s}^{-1}$, then the heat capacity at constant pressure is: (Take gas constant R=8.3 JK^-1mol^-1)

(1) 8.0 JK^-1mol^-1
 

(2) 7.5 JK^-1mol^-1
 

(3) 7.0 JK^-1mol^-1
 

(4) 8.5 JK^-1mol^-1

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) $\frac{2}{3}\mathrm{\pi }$

Sound waves have the following frequencies that are audible to human beings :

1. 5 c/s

2. 27000 c/s

3. 5000 c/s

4. 50,000 c/s

The minimum audible wavelength at room temperature is about

1. 0.2 Å

2. 5 Å

3 5 cm to 2 metre

4. 20 mm

The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is 

1.  $\sqrt{2/7}$

2.  $\sqrt{1/7}$

3.  $\sqrt{3}/5$

4.  $\sqrt{6}/5$

The frequency of a rod is 200 Hz. If the velocity of sound in air is 340 ms^–1, the wavelength of the sound produced is :

1. 1.7 cm

2. 6.8 cm

3. 1.7 m

4. 6.8 m