$A$ railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer standing beside the railway track. The frequency $(n)$ of the sound heard by the observer is plotted against time $(t).$ Which of the following best represents the resulting curve?

$A$ 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 $m/s$.

Which of the following statements is false?

$A$ vibrating tuning fork is moving slowly and uniformly in a horizontal circular path of radius $8 \, m$. The shortest distance of an observer in the same plane from the tuning fork is $9 \, m$. The distance between the tuning fork and the observer at the instant when the apparent frequency becomes maximum is ......... $m$.

An engine moving away from a vertical cliff blows a horn at a frequency $f$. Its speed is $0.5 \%$ of the speed of sound in air. The frequency of the reflected sound received at the engine is ............ $f$.

$A$ source of sound $S$ of frequency $500 \ Hz$ situated between a stationary observer $O$ and a wall $W$,moves towards the wall with a speed of $2 \ m/s$. If the velocity of sound is $332 \ m/s$,then the number of beats per second heard by the observer is (approximately)