$A$ car $P$ travelling at $20\,ms^{-1}$ sounds its horn at a frequency of $400\,Hz$. Another car $Q$ is travelling behind the first car in the same direction with a velocity $40\,ms^{-1}$. The frequency heard by the passenger of the car $Q$ is approximately $.......\,Hz$. [Take,velocity of sound $= 360\,ms^{-1}$]

An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$th that of sound. The frequency of the sound emitted by the source is $f$. The apparent frequency recorded by the observer is

$A$ stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2 \ m/s$ in front of the open end of the pipe and parallel to it,the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320 \ m/s$,the smallest value of the percentage change required in the length of the pipe is. . . . . .

The speed of sound in air at a given temperature is $350 \, m/s$. An engine blows a whistle at a frequency of $1200 \, cps$. It is approaching the observer with a velocity of $50 \, m/s$. The apparent frequency in $cps$ heard by the observer will be:

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed of $1.0 \,m \,s^{-1}$ and the man behind walks at a speed of $2.0 \,m \,s^{-1}$. $A$ third man is standing at a height of $12 \,m$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $1430 \,Hz$. The speed of sound in air is $330 \,m \,s^{-1}$. At the instant when the moving men are $10 \,m$ apart,the stationary man is equidistant from them. The frequency of beats in $Hz$ heard by the stationary man at this instant is:

$A$ source of sound of frequency $500 Hz$ is moving towards an observer with velocity $30 m/s$. The speed of sound is $330 m/s$. The frequency heard by the observer will be .... $Hz$