$A$ train moving at a speed of $220\, m s^{-1}$ towards a stationary object,emits a sound of frequency $1000\, Hz$. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is ...... $Hz$. (Speed of sound in air is $330\, m s^{-1}$)

$A$ car travelling at a speed of $54 \ km/h$ towards a wall sounds a horn of frequency $400 \ Hz$. The difference in the frequencies of two sounds, one received directly from the car and the other reflected from the wall, noticed by a person standing between the car and the wall is (speed of sound in air is $335 \ m/s$):

$S_1$ 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 $\qquad$ $Hz$.

An observer moves towards a stationary source of sound,with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

$A$ source and an observer approach each other with the same velocity $50 \, m/s$. If the apparent frequency is $435 \, s^{-1}$,then the real frequency is .... $s^{-1}$ (Take speed of sound $v = 332 \, m/s$)

The velocity of sound is $340 \,m/s$. $A$ source of sound having a frequency of $90 \,Hz$ is moving towards a stationary observer with a speed of one-tenth that of sound. The apparent frequency of sound as heard by the observer is: (in $\,Hz$)