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 .... $m$

A string of mass $2.5\ kg$ is under a tension of $200\ N$ . The length of the stretched string is $20.0\ m$ . If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in .... $\sec$

An engine approaches a hill with a constant speed. When it is at a distance of $0.9 km$ it blows a whistle, whose echo is heard by the driver after $5$ sec. If speed of sound in air is $330 m/s$, the speed of engine is .... $m/s$

A transverse harmonic wave on a string is described by $y = 3\sin \left( {36t + 0.018x + \frac{\pi }{4}} \right)$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two successive crests in the wave is .... $m$

Four sources of sound each of sound level $10\,dB$ are sounded together, there sultant intensity level will be ... $dB$

A car $P$ approaching a crossing at a speed of $10\,m/s$ sounds a horn of frequency $700 \,Hz$ when $40\,m$ in front of the crossing. Speed of sound in air is $340\,m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\,m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ..... $Hz$