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. \(8\)

Equation of the wave is given by y = 0.4 sin(314t - 3.14x), where x and y are in meter and t is in second. The speed of the wave is :

1.  50 m/s

2.  100 m/s

3.  314 m/s

4.  3.14 m/s

A plane progressive wave cannot be represented by

1.  $\mathrm{y}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\mathrm{a}<mspace\; width="1em"></mspace>\sin <mspace\; width="1em"></mspace>\left(\mathrm{\omega t}<mspace\; width="1em"></mspace>\pm <mspace\; width="1em"></mspace>\mathrm{kx}\right)<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

2.  $\mathrm{y}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\mathrm{a}<mspace\; width="1em"></mspace>\sin <mspace\; width="1em"></mspace>2\mathrm{\pi }\left(\frac{\mathrm{t}}{\mathrm{T}}\mp <mspace\; width="1em"></mspace>\frac{\mathrm{x}}{\lambda }\right)<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $\mathrm{y}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\mathrm{a}<mspace\; width="1em"></mspace>\sin <mspace\; width="1em"></mspace>\frac{2\mathrm{\pi }}{\mathrm{\lambda }}<mspace\; width="1em"></mspace>\left(\mathrm{Vt}<mspace\; width="1em"></mspace>\mp <mspace\; width="1em"></mspace>\mathrm{x}\right)<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4.  $\mathrm{y}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\mathrm{A}<mspace\; width="1em"></mspace>\log <mspace\; width="1em"></mspace>\mathrm{x}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\mathrm{B}<mspace\; width="1em"></mspace>\log <mspace\; width="1em"></mspace>\mathrm{x}$

The phase difference between the prongs of a tuning fork is :

1.  $2\mathrm{\pi }<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

2.  $3\mathrm{\pi }<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $\mathrm{\pi }<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4.  $5\mathrm{\pi }$

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.  ${\mathrm{E}}_{\mathrm{i}}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

2.  ${\mathrm{E}}_{\mathrm{a}}<mspace\; width="1em"></mspace>$

3.  $\sqrt{{\mathrm{E}}_{\mathrm{i}}}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

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

When a wave is reflected from a denser medium the change in phase is :

1.  0

2.  $\mathrm{\pi }<mspace\; width="1em"></mspace>$

3.  $2\mathrm{\pi }<mspace\; width="1em"></mspace>$

4.  $3\mathrm{\pi }$

In a stationary wave along a string, the strain is:
1. zero at the antinodes
2. maximum at the antinodes
3. zero at the nodes
4. maximum at the nodes

A source of sound moves away with the velocity of sound from a stationary observer. The frequency of the sound heard by the observer:

1. remains the same

2. is doubled

3. is halved

4. becomes infinity
 

The longitudinal waves can travel :

1.  only in liquids

2.  only in solids

3.  only in gases

4.  In liquids, solids, and gases

The equation of a wave pulse travelling along x-axis is given by $y=\frac{30}{2+{\left(x-20t\right)}^2}$, x and y are in meters and t is in seconds. The amplitude of the wave pulse is 

1.  5 m

2.  20 m

3.  15 m

4.  30 m