$A$ whistle $S$ of frequency $f$ revolves in a circle of radius $R$ at a constant speed $v$. What is the ratio of maximum and minimum frequency detected by a detector $D$ at rest at a distance $2R$ from the center of the circle as shown in the figure?

Two vehicles,each moving with speed $u$ on the same horizontal straight road,are approaching each other. Wind blows along the road with velocity $w$. One of these vehicles blows a whistle of frequency $f_1$. An observer in the other vehicle hears the frequency of the whistle to be $f_2$. The speed of sound in still air is $V$. The correct statement$(s)$ is (are) :
$(A)$ If the wind blows from the observer to the source,$f_2 > f_1$.
$(B)$ If the wind blows from the source to the observer,$f_2 > f_1$.
$(C)$ If the wind blows from the observer to the source,$f_2 < f_1$.
$(D)$ If the wind blows from the source to the observer,$f_2 < f_1$.

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

$A$ small source of sound moves on a circle as shown in the figure and an observer is standing at $O.$ Let $n_1, n_2$ and $n_3$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. Then

$A$ source of sound of frequency $640 \,Hz$ is moving at a velocity of $\frac{100}{3} \,m/s$ along a road, and is at an instant $30 \,m$ away from a point $A$ on the road. $A$ person standing at $O$, $40 \,m$ away from the road, hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 \,m/s$): (in $\,Hz$)

$A$ boy is walking away from a wall towards an observer at a speed of $1\, m/s$ and blows a whistle whose frequency is $680\, Hz$. The number of beats heard by the observer per second is (Velocity of sound in air $= 340\, m/s$).