$A$ source at rest emits sound waves of frequency $102 \ Hz$. Two observers are moving away from the source of sound in opposite directions, each with a speed of $10 \%$ of the speed of sound. The ratio of the frequencies of sound heard by the observers is

Consider the Doppler effect in two cases. In the first case,an observer moves towards a stationary source of sound with a speed of $50 \,m/s$. In the second case,the observer is at rest and the source moves towards the observer with the same speed of $50 \,m/s$. Then the frequency heard by the observer will be [velocity of sound in air $= 330 \,m/s$.]

The frequency of a whistle of an engine is $600 \, Hz$ and it is moving with a speed of $30 \, m/s$ towards a stationary observer. The apparent frequency heard by the observer will be .... $Hz$ (velocity of sound $= 330 \, m/s$).

$A$ 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 $, Hz$)

$A$ bat is flitting about in a cave,navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is $40\; kHz$. During one fast swoop directly toward a flat wall surface,the bat is moving at $0.03$ times the speed of sound in air. What frequency (in $kHz$) does the bat hear reflected off the wall?

$A$ person feels a $2.5\%$ difference in the frequency of a motor-car horn. If the motor-car is moving towards the person and the velocity of sound is $320\, m/s$,then the velocity of the car will be: