Two tuning forks having frequency $256\, Hz \,(A)$ and $262\, Hz \,(B)$ tuning fork. $A$ produces some beats per second with unknown tuning fork, same unknown tuning fork  produce double beats per second from $B$ tuning fork then the frequency of unknown tuning fork is :- ............ $\mathrm{Hz}$

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 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 ...... $Hz$

Beats are produced by two waves $y_1 = a\, sin\, (1000\, \pi t)$ and $y^2 = a\, sin\, (998\, \pi t)$ The number of beats heard per second is

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 .... $\sec$

The two waves represented by $y_1 = a\,sin(\omega\,t)$ and $y_2 = b\, cos\, (\omega\, t)$ have a phase difference of