$A$ 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:

$A$ source emitting sound of frequency $288 \,Hz$ is tied to a string of $100 \,cm$ length and rotated with an angular velocity of $20 \,rad/s$ in the horizontal plane. The range of frequencies heard by an observer standing at a distance of $5 \,m$ from the source is (in $Hz$) (Speed of sound in air $= 340 \,m/s$)

$A$ train is moving towards a stationary observer. Which of the following curves best represents the frequency $f$ received by the observer as a function of time $t$?

Two trains are moving towards each other at speeds of $20 \, m/s$ and $15 \, m/s$ relative to the ground. The first train sounds a whistle of frequency $600 \, Hz$. The frequency of the whistle heard by a passenger in the second train before the trains meet is ...... $Hz$ (the speed of sound in air is $340 \, m/s$).

An audio transmitter $(T)$ and a receiver $(R)$ are hung vertically from two identical massless strings of length $8 \ m$ with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular amplitude $\theta_0 = \cos^{-1}(0.9)$ and released simultaneously. If the natural frequency of the transmitter is $660 \ Hz$ and the speed of sound in air is $330 \ m/s$,the maximum variation in the frequency (in $Hz$) as measured by the receiver (Take the acceleration due to gravity $g = 10 \ m/s^2$) is:

$A$ source,approaching with speed $u$ towards the open end of a stationary pipe of length $L$,is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination$(s)$ of $u$ and $f_s$,will the sound reaching the pipe lead to a resonance?
$(A)$ $u=0.8 v$ and $f_s=f_0$
$(B)$ $u=0.8 v$ and $f_s=2 f_0$
$(C)$ $u=0.8 v$ and $f_s=0.5 f_0$
$(D)$ $u=0.5 v$ and $f_s=1.5 f_0$