$A$ whistle of frequency $660 \,Hz$ moves in a circle of radius $1 \,m$ at an angular speed of $10 \,rad/s$. The highest frequency heard by a listener at a long distance and at rest with respect to the center of the circle is (Let speed of sound $= 340 \,m/s$.) (in $\,Hz$)

$A$ source $S$ emitting sound of frequency $288 \,Hz$ is fixed on block $B$ which is attached to the free end of a spring $S_2$, and an observer $O$ is on block $A$ which is attached to the free end of spring $S_1$ as shown in the figure. The blocks $A$ and $B$ are simultaneously displaced towards each other through a distance of $0.5 \,m$ and then left to oscillate. If the angular velocity of each block is $40 \,rad/s$, then the maximum frequency observed by the observer is (speed of sound in air is $340 \,m/s$): (in $\,Hz$)

$A$ source of sound $S$ is moving with a velocity $50 \ m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000 \ Hz$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of sound in the medium is $350 \ m/s$.

$A$ sound source is moving in a circle and an observer is outside the circle at $O$ as shown in the figure. If the frequencies as heard by the listener are $\nu_1, \nu_2$ and $\nu_3$ when the source is at positions $A, B$ and $C$ respectively,then:

Two sources $A$ and $B$ are producing notes of frequency $680 \,Hz$. $A$ listener moves from $A$ to $B$ with a constant velocity $v$. If the speed of sound in air is $340 \,ms^{-1}$, the value of $v$ so that he hears $10$ beats per second is: (in $\,ms^{-1}$)

$A$ 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. The 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. 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 ..... $Hz$.