An engine is moving on a circular path of radius $200 \,m$ with a speed of $15 \,m/s$. What will be the frequency heard by an observer who is at rest at the centre of the circular path,when the engine blows the whistle with a frequency of $250 \,Hz$?

$A$ whistle of frequency $540 Hz$ rotates in a horizontal circle of radius $2 m$ at an angular speed of $15 rad/s$. What is the highest frequency heard by a listener at rest with respect to the center of the circle (in $Hz$)? (Velocity of sound in air $= 330 m/s$)

$A$ 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 $f_s=1.5 f_0$

$A$ man is standing between two trains moving away from and towards him,both with a speed of $4 \, m/s$. If both trains produce a sound of frequency $240 \, Hz$,calculate the number of beats heard by the man. (Speed of sound in air = $320 \, m/s$)

Statement $-1$: Due to the motion of the listener,the frequency of the sound waves (as received by the listener) emitted by a stationary source is affected.
Statement $-2$: Due to the motion of the source,the wavelength of the sound waves (emitted by the source) as received by a stationary listener is affected.
Statement $-3$: If the receiver and the source are both moving,the observed frequency must be different from the original frequency of the source.
Treat the motion of the source or listener as always along the line joining them for all the above cases.

$A$ train blowing the whistle moves with a constant velocity $V$ away from an observer standing on the platform. The ratio of the natural frequency of the whistle $n$ to the apparent frequency is $1.2: 1$. If the train is at rest and the observer moves away from it at the same velocity $V$,the ratio of $n$ to the apparent frequency is (in $: 1$)