Two cars $A$ and $B$ are moving away from each other in opposite directions. Both cars are moving with a speed of $20 \, ms^{-1}$ with respect to the ground. If an observer in car $A$ detects a frequency of $2000 \, Hz$ from the sound source in car $B$,what is the natural frequency of the sound source of car $B$ (in $Hz$)? (Speed of sound in air $= 340 \, ms^{-1}$)

$S_1$ and $S_2$ are two identical sound sources of frequency $656 \ Hz$. The source $S_1$ is located at $O$ and $S_2$ moves anti-clockwise with a uniform speed $4 \sqrt{2} \ ms^{-1}$ on a circular path around $O$,as shown in the figure. There are three points $P, Q$ and $R$ on this path such that $P$ and $R$ are diametrically opposite while $Q$ is equidistant from them. $A$ sound detector is placed at point $P$. The source $S_1$ can move along direction $OP$.
[Given: The speed of sound in air is $324 \ ms^{-1}$]
$(1)$ When only $S_2$ is emitting sound and it is at $Q$,the frequency of sound measured by the detector in $Hz$ is. . . . . .
$(2)$ Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4 \ ms^{-1}$,the beat frequency measured by the detector is $\qquad$ $Hz$.

$A$ whistle revolves in a circle with an angular speed of $20 \; rad/s$ using a string of length $50 \; cm.$ If the frequency of sound from the whistle is $385 \; Hz,$ then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? $(v = 340 \; m/s)$

$A$ stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2 \ m/s$ in front of the open end of the pipe and parallel to it,the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320 \ m/s$,the smallest value of the percentage change required in the length of the pipe is. . . . . .

$A$ 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 emits a sound of frequency $400 \ Hz$,but the listener hears it to be $390 \ Hz$. Then: