$A$ $SONAR$ system fixed in a submarine operates at a frequency of $40.0 \; kHz$. An enemy submarine moves towards the $SONAR$ with a speed of $360 \; km/h$. What is the frequency (in $kHz$) of sound reflected by the submarine (in $; kHz$)? Take the speed of sound in water to be $1450 \; m/s$.

$A$ train whistling at a constant frequency is moving towards a station at a constant speed $V_S$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.

$A$ source producing sound of frequency $170 \, Hz$ is approaching a stationary observer with a velocity $17 \, ms^{-1}$. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air $= 340 \, ms^{-1}$) ..... $m$

When an engine passes near a stationary observer,its apparent frequencies occur in the ratio $5/3$. If the velocity of sound is $340 \ m/s$,then the velocity of the engine is .... $m/s$.

$A$ car sounding a horn of frequency $1000 \,Hz$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is $11:9$. The speed of the car is (Speed of sound $v = 340 \,ms^{-1}$) (in $\,ms^{-1}$)

$A$ rocket is moving at a speed of $200\; m s^{-1}$ towards a stationary target. While moving, it emits a wave of frequency $1000\; Hz$. Some of the sound reaching the target gets reflected back to the rocket as an echo. Calculate:
$(1)$ the frequency of the sound as detected by the target and
$(2)$ the frequency of the echo as detected by the rocket.