$A$ vibrating tuning fork is moving slowly and uniformly in a horizontal circular path of radius $8 \, m$. The shortest distance of an observer in the same plane from the tuning fork is $9 \, m$. The distance between the tuning fork and the observer at the instant when the apparent frequency becomes maximum is ......... $m$.

$A$ sounding body of negligible dimension emitting a frequency of $150\, Hz$ is dropped from a height. During its fall under gravity,it passes near a balloon moving up with a constant velocity of $2\, m/s$ one second after it started to fall. The difference in the frequency observed by the man in the balloon just before and just after crossing the body will be: (Given: velocity of sound $= 300\, m/s$; $g = 10\, m/s^2$) (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 $\,Hz$)

Two cars moving in opposite directions approach each other with speeds of $22 \, m s^{-1}$ and $16.5 \, m s^{-1}$ respectively. The driver of the first car blows a horn having a frequency of $400 \, Hz$. The frequency heard by the driver of the second car is ..... $Hz$ (velocity of sound is $340 \, m s^{-1}$)

$A$ source $(S)$ of sound has a frequency of $240 \ Hz$. When the observer $(O)$ and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case $1$ in the figure),the observer measures the frequency of the sound to be $288 \ Hz$. However,when the observer and the source move away from each other at the same speed $v$ with respect to the ground (as shown in Case $2$ in the figure),the observer measures the frequency of the sound to be $n \ Hz$. The value of $n$ is:

Two sources $A$ and $B$ are sounding notes of frequency $660 \, Hz$. $A$ listener moves from $A$ to $B$ with a constant velocity $u$. If the speed of sound is $330 \, m/s$,what must be the value of $u$ so that he hears $8$ beats per second?