$A$ detector is released from rest over a source of sound of frequency $f_0 = 10^3 \, Hz$. The frequency observed by the detector at time $t$ is plotted in the graph. Given $g = 10 \, m/s^2$,find the speed of sound in air in $m/s$.

$A$ policeman on duty detects a drop of $10 \%$ in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is $330 \, m/s$,calculate the speed of the car in $m/s$.

$A$ whistle $S$ of frequency $f$ revolves in a circle of radius $R$ at a constant speed $v$. What is the ratio of maximum and minimum frequency detected by a detector $D$ at rest at a distance $2R$ from the center of the circle as shown in the figure?

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:

$A$ speaker emits a sound wave of frequency $f_0$. When it moves towards a stationary observer with speed $u$,the observer measures a frequency $f_1$. If the speaker is stationary and the observer moves towards it with speed $u$,the measured frequency is $f_2$. Then,

When the observer moves towards a stationary source with velocity $V_1$,the apparent frequency of the emitted note is $F_1$. When the observer moves away from the source with velocity $V_1$,the apparent frequency is $F_2$. If $V$ is the velocity of sound in air and $F_1 / F_2 = 2$,then $V / V_1$ is equal to: