Two cars $A$ and $B$ are moving in the same direction with speeds $36\, km/hr$ and $54 \,km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds horn of frequency  $1000\, Hz$ and the speed of sound in air is $340\, m/s$, the frequency of sound  received by the driver of car $B$ is ..... $Hz$

Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

Which of the following is correct ?

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 ..... $Hz$

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9$ meters and $25$ meters respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

Two waves of sound having intensities $I$ and $4I$ interfere to produce interference pattern. The phase difference between the waves is $\pi /2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is