$A$ 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 $m/s$.

An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is ..... $\%$

$A$ stationary source is emitting sound at a fixed frequency $f_0$,which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2\%$ of $f_0$. What is the difference in the speeds of the cars (in $km/h$) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound,which is $330 \ m/s$.

$A$ source of sound emits waves with frequency $f \, Hz$ and speed $V \, m/s$. Two observers move away from this source in opposite directions,each with a speed $0.2V$ relative to the source. The ratio of frequencies heard by the two observers will be

$A$ source of sound $S$ is moving with a velocity $50 \ m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000 \ Hz$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of sound in the medium is $350 \ m/s$.

Two factories are sounding their sirens at $800 \, Hz$. $A$ man walks from one factory to the other at a speed of $2 \, m/s$. The velocity of sound is $320 \, m/s$. The number of beats heard by the person in one second will be: