Consider two tuning forks with natural frequency $250 \,Hz$. One is moving away and another is moving towards a stationary observer at the same speed. If the observer hears beats of frequency $5 \,Hz$, then the speed of the tuning fork is: (Given, speed of sound wave is $350 \,m/s$.) (in $\,m/s$)

Obtain the equation for the frequency observed by a stationary observer when the source is moving.

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:

$A$ train whistling at a constant frequency is moving towards a station at a constant speed $V_S$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.

Two whistles $A$ and $B$ produce notes of frequencies $660 \ Hz$ and $596 \ Hz$ respectively. There is a listener at the mid-point of the line joining them. Now,the whistle $B$ and the listener start moving with a speed of $30 \ m/s$ away from the whistle $A$. If the speed of sound is $330 \ m/s$,how many beats will be heard by the listener?

An engine moving towards a wall with a velocity $50 \ m/s$ emits a note of $1.2 \ kHz$. The speed of sound in air is $350 \ m/s$. The frequency of the note after reflection from the wall as heard by the driver of the engine is: (in $kHz$)