A man fires a bullet standing between two cliffs. First echo is heard after $3\, seconds$ and second echo is heard after $5\, seconds$. If the velocity of sound is $330\,m/s$, then the distance between the cliffs is …. $m$

Two identical sounds $S_1$ and $S_2$ reach at a point $P$ in phase. The resultant loudness at point $P$ is $n\,\, dB$  higher than the loudness of $S_1$. The value of $n$ is

The amplitude of a wave disturbance propagating in the positive $X-$ direction is given by $y = 1/(1 + x^2)$ at time $t = 0$ and by $y = 1/[1 + (x -1)^2]$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ….. $ms^{-1}$

A plan wave of sound traveling in air is incident upon a plan surface of a liquid. The angle of incidence is $60^o$. The speed of sound in air is $300\ m/s$ and in the liquid it is $600\ m/s$. Assume Snell's law to be valid for sound waves 

The diagram shows snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. Direction of propagation of wave is