An observer standing at a station observes a frequency of $219 \, Hz$ when a train approaches and $184 \, Hz$ when the train goes away from him. If the velocity of sound in air is $340 \, m/s$,then the velocity of the train and the actual frequency of the whistle will be:

$A$ sound source is moving on a circular path of radius $R$ with constant angular speed $\omega$ in an anticlockwise direction and emits a frequency $n$. An observer performs simple harmonic motion along the path $QPR$ with time period $T = \frac{2\pi}{\omega}$ as shown in the figure. If at $t = 0$ the source is at $A$ and the observer is at $Q$,and assuming $OP$ is very large compared to the radius $R$ and $QP$,then:

$A$ source is moving towards an observer with a speed of $20 \ m/s$ and having a frequency of $240 \ Hz$. The observer is now moving towards the source with a speed of $20 \ m/s$. If the velocity of sound is $340 \ m/s$,the apparent frequency heard by the observer is ... $Hz$.

$A$ 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 $, Hz$)

$A$ stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed $v$ (much less than the speed of sound). The observer hears $2 \; \text{beats/sec}$. The oscillation frequency of each tuning fork is $\nu_{0} = 1400 \; \text{Hz}$ and the velocity of sound in air is $c = 350 \; \text{m/s}$. The speed of each tuning fork is close to:

$A$ 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 $= 340 \,m/s$)